First, a class of higher order exponential type hybrid (α,β, γ, η, p, h(.,.), κ(., .), w(.,., .), ω(.,.,.), θ)-invexities is introduced, second, some parametrically sufficient efficiency conditions ba...First, a class of higher order exponential type hybrid (α,β, γ, η, p, h(.,.), κ(., .), w(.,., .), ω(.,.,.), θ)-invexities is introduced, second, some parametrically sufficient efficiency conditions based on the higher order exponential type hybrid invexities are established, and finally some parametrically sufficient efficiency results under the higher order exponential type hybrid (a,β, γ, ρ, h(.,.), k(.,-), w(-,., .), w(.,., .), 0)-invexities are investigated to the context of solving semiinfinite multiobjective fractional programming problems. The notions of the higher order exponential type hybrid (a, β, γ η, p, h(., .), n(., .), w(-,.,-), ω(.,.,.), 0)-invexities encompass most of the generalized invexities in the literature. To the best of our knowledge, the results on semiinfinite multiobjective fractional programming problems established in this communication are new and application-oriented toward multitime multi- objectve problems as well as multiobiective control problems.展开更多
A new concept of(Φ,ρ,α)-V-invexity for differentiable vector-valued functions is introduced,which is a generalization of differentiable scalar-valued(Φ,ρ)-invexity.Based upon the(Φ,ρ,α)-V-invex functions,suffi...A new concept of(Φ,ρ,α)-V-invexity for differentiable vector-valued functions is introduced,which is a generalization of differentiable scalar-valued(Φ,ρ)-invexity.Based upon the(Φ,ρ,α)-V-invex functions,sufficient optimality conditions and MondWeir type dual theorems are derived for a class of nondifferentiable multiobjective fractional programming problems in which every component of the objective function and each constraint function contain a term involving the support function of a compact convex set.展开更多
This paper studies a class of multiobjective generalized fractional programming problems, where the numerators of objective functions are the sum of differentiable function and convex function, while the denominators ...This paper studies a class of multiobjective generalized fractional programming problems, where the numerators of objective functions are the sum of differentiable function and convex function, while the denominators are the difference of differentiable function and convex function. Under the assumption of Calmness Constraint Qualification the Kuhn-Tucker type necessary conditions for efficient solution are given, and the Kuhn-Tucker type sufficient conditions for efficient solution are presented under the assumptions of (F, α, ρ, d)-V-convexity. Subsequently, the optimality conditions for two kinds of duality models are formulated and duality theorems are proved.展开更多
In this paper, two duality results are established under generalized ρ-convexity conditions for a class of multiobjective fractional programmign involvign differentiable n-sten functions.
The mixed-integer quadratically constrained quadratic fractional programming(MIQCQFP)problem often appears in various fields such as engineering practice,management science and network communication.However,most of th...The mixed-integer quadratically constrained quadratic fractional programming(MIQCQFP)problem often appears in various fields such as engineering practice,management science and network communication.However,most of the solutions to such problems are often designed for their unique circumstances.This paper puts forward a new global optimization algorithm for solving the problem MIQCQFP.We first convert the MIQCQFP into an equivalent generalized bilinear fractional programming(EIGBFP)problem with integer variables.Secondly,we linearly underestimate and linearly overestimate the quadratic functions in the numerator and the denominator respectively,and then give a linear fractional relaxation technique for EIGBFP on the basis of non-negative numerator.After that,combining rectangular adjustment-segmentation technique and midpointsampling strategy with the branch-and-bound procedure,an efficient algorithm for solving MIQCQFP globally is proposed.Finally,a series of test problems are given to illustrate the effectiveness,feasibility and other performance of this algorithm.展开更多
This paper aims at studying optimality conditions of robust weak efficient solutions for a nonsmooth uncertain multi-objective fractional programming problem(NUMFP).The concepts of two types of generalized convex func...This paper aims at studying optimality conditions of robust weak efficient solutions for a nonsmooth uncertain multi-objective fractional programming problem(NUMFP).The concepts of two types of generalized convex function pairs,called type-I functions and pseudo-quasi-type-I functions,are introduced in this paper for(NUMFP).Under the assumption that(NUMFP)satisfies the robust constraint qualification with respect to Clarke subdifferential,necessary optimality conditions of the robust weak efficient solution are given.Sufficient optimality conditions are obtained under pseudo-quasi-type-I generalized convexity assumption.Furthermore,we introduce the concept of robust weak saddle points to(NUMFP),and prove two theorems about robust weak saddle points.The main results in the present paper are verified by concrete examples.展开更多
This paper presents an efficient algorithm for globally solving a generalized linear fractional programming problem.For establishing this algorithm,we firstly construct a two-level linear relaxation method,and by util...This paper presents an efficient algorithm for globally solving a generalized linear fractional programming problem.For establishing this algorithm,we firstly construct a two-level linear relaxation method,and by utilizing the method,we can convert the initial generalized linear fractional programming problem and its subproblems into a series of linear programming relaxation problems.Based on the branch-and-bound framework and linear programming relaxation problems,a branch-and-bound algorithm is presented for globally solving the generalized linear fractional programming problem,and the computational complexity of the algorithm is given.Finally,numerical experimental results demonstrate the feasibility and efficiency of the proposed algorithm.展开更多
A semi-infinite programming problem is a mathematical programming problem with a finite number of variables and infinitely many constraints. Duality theories and generalized convexity concepts are important research t...A semi-infinite programming problem is a mathematical programming problem with a finite number of variables and infinitely many constraints. Duality theories and generalized convexity concepts are important research topics in mathematical programming. In this paper, we discuss a fairly large number of paramet- ric duality results under various generalized (η,ρ)-invexity assumptions for a semi-infinite minmax fractional programming problem.展开更多
For optimizing the water-use structure and increasing plantation benefit of unit water consumption,a multi-objective model for water resources utilization was established based on fractional programming(FP).Meanwhile,...For optimizing the water-use structure and increasing plantation benefit of unit water consumption,a multi-objective model for water resources utilization was established based on fractional programming(FP).Meanwhile,considering the stochasticity of water availability in the study area,the impact of the risk factor(λ)from a quantitative and qualitative perspective was analyzed.The chance-constrained programming(CCP)and conditional value-at-risk(CVaR)models were introduced into five important major grain production areas in Sanjiang Plain,and the crop planting structure under this condition was optimized.The results showed that,after optimization,overall benefit of cultivation increased from 42.07 billion Yuan to 42.47 billion Yuan,water consumption decreased from 15.90 billion m3 to 11.95 billion m3,the plantation benefit of unit water consumption increased from 2.65 Yuan/m3 to 3.55 Yuan/m3.Furthermore,the index of water consumption,benefit of cultivation and plantation benefit of unit water consumption showed an increasing trend with the increase of violation likelihood.However,through the quantification ofλfrom an economic perspective,the increasing ofλcould not enhance plantation benefit of unit water consumption significantly.展开更多
In this paper, we discuss a large number of sets of global parametric sufficient optimality conditions under various generalized (η,ρ)-invexity assumptions for a semi-infinite minmax fractional programming problem.
In this paper, we present several parametric duality results under various generalized (a,v,p)-V- invexity assumptions for a semiinfinite multiobjective fractional programming problem.
Abstract In this paper, we discuss numerous sets of global parametric sufficient efficiency conditions under various generalized (a,n, p)-V-invexity assumptions for a semiinfinite multiobjective fractional programmi...Abstract In this paper, we discuss numerous sets of global parametric sufficient efficiency conditions under various generalized (a,n, p)-V-invexity assumptions for a semiinfinite multiobjective fractional programming problem.展开更多
In Non-Orthogonal Multiple Access(NOMA),the best way to fully exploit the benefits of the system is the efficient resource allocation.For the NOMA power domain,the allocation of power and spectrum require solving the ...In Non-Orthogonal Multiple Access(NOMA),the best way to fully exploit the benefits of the system is the efficient resource allocation.For the NOMA power domain,the allocation of power and spectrum require solving the mixed-integer nonlinear programming NP-hard problem.In this paper,we investigate user scheduling and power allocation in Multi-Cell Multi-Carrier NOMA(MCMC-NOMA)networks.To achieve that,we consider Weighted Sum Rate Maximization(WSRM)and Weighted Sum Energy Efficiency Maximization(WSEEM)problems.First,we tackle the problem of user scheduling for fixed power using Fractional Programming(FP),the Lagrange dual method,and the decomposition method.Then,we consider Successive Pseudo-Convex Approximation(SPCA)to deal with the WSRM problem.Finally,for the WSEEM problem,SPCA is utilized to convert the problem into separable scalar problems,which can be parallelly solved.Thus,the Dinkelbach algorithm and constraints relaxation are used to characterize the closed-form solution for power allocation.Extensive simulations have been implemented to show the efficiency of the proposed framework and its superiority over other existing schemes.展开更多
In this paper,we investigate the reconfigurable intelligent surface(RIS)-enabled multiple-input-single-output orthogonal frequency division multiplexing(MISO-OFDM)system under frequency-selective channels,and propose ...In this paper,we investigate the reconfigurable intelligent surface(RIS)-enabled multiple-input-single-output orthogonal frequency division multiplexing(MISO-OFDM)system under frequency-selective channels,and propose a low-complexity alternating optimization(AO)based joint beamforming and RIS phase shifts optimization algorithm to maximize the achievable rate.First,with fixed RIS phase shifts,we devise the optimal closedform transmit beamforming vectors corresponding to different subcarriers.Then,with given active beamforming vectors,near-optimal RIS reflection coefficients can be determined efficiently leveraging fractional programming(FP)combined with manifold optimization(MO)or majorization-minimization(MM)framework.Additionally,we also propose a heuristic RIS phase shifts design approach based on the sum of subcarrier gain maximization(SSGM)criterion requiring lower complexity.Numerical results indicate that the proposed MO/MM algorithm can achieve almost the same rate as the upper bound achieved by the semidefinite relaxation(SDR)algorithm,and the proposed SSGM based scheme is only slightly inferior to the upper bound while has much lower complexity.These results demonstrate the effectiveness of the proposed algorithms.展开更多
In this paper, proportional fairness(PF)-based energy-efficient power allocation is studied for multiple-input multiple-output(MIMO) non-orthogonal multiple access(NOMA) systems. In our schemes, statistical channel st...In this paper, proportional fairness(PF)-based energy-efficient power allocation is studied for multiple-input multiple-output(MIMO) non-orthogonal multiple access(NOMA) systems. In our schemes, statistical channel state information(CSI) is utilized for perfect CSI is impossible to achieve in practice. PF is used to balance the transmission efficiency and user fairness. Energy efficiency(EE) is formulated under basic data rate requirements and maximum transmitting power constraints. Due to the non-convex nature of EE, a two-step algorithm is proposed to obtain sub-optimal solution with a low complexity. Firstly, power allocation is determined by golden section search for fixed power. Secondly total transmitting power is determined by fractional programming method in the feasible regions. Compared to the performance of MIMO-NOMA without PF constraint, fairness is obtained at expense of decreasing of EE.展开更多
The efficient antenna scheduling strategy for data relay satellites(DRSs)is essential to optimize the throughput or delay of the satellite data relay network.However,these two objectives conflict with each other since...The efficient antenna scheduling strategy for data relay satellites(DRSs)is essential to optimize the throughput or delay of the satellite data relay network.However,these two objectives conflict with each other since the user satellites(USs)with higher priorities take up more transmission time of DRSs’antennas for greater throughput but the USs storing more packets cause a severer waiting delay to the whole network.To balance the conflicting metrics for meeting the delay-throughput integrated requirements,we formulate the antenna scheduling as a stochastic non-convex fractional programming,which is challenging to be solved.For the tractability,we equivalently transform the fractional programming to a parametric problem and implement the Lyapunov drift to guarantee the constraint of mean rate stability.By proposing a delay and throughput tradeoff based antenna scheduling algorithm,we further transform the parametric problem to a solvable weight matching problem.Simulation results reveal the feasible region of the preference control parameter for integrated QoS cases and its variation relationship with network delay and throughput.展开更多
The energy efficiency(EE) for the full-duplex massive multi-input multi-output(MIMO) system is investigated. Given the transmit powers of both the uplink and the downlink, the closed-form solutions of the optimal ...The energy efficiency(EE) for the full-duplex massive multi-input multi-output(MIMO) system is investigated. Given the transmit powers of both the uplink and the downlink, the closed-form solutions of the optimal number of antennas and the maximum EE are achieved in the high regime of the signal-to-noise ratio(SNR). It is shown that the optimal number of antennas and the maximum EE gets larger with the increase in user numbers. To further improve the EE, an optimization algorithm with low complexity is proposed to jointly determine the number of antennas and the transmit powers of both the uplink and the downlink. It is shown that, the proposed algorithm can achieve the system performance very close to the exhaustive search.展开更多
If Hall plates are used as magnetic field sensors they are usually powered up by a current source connected to a pair of non-neighboring contacts. The output voltage is tapped at another pair of non-neighboring contac...If Hall plates are used as magnetic field sensors they are usually powered up by a current source connected to a pair of non-neighboring contacts. The output voltage is tapped at another pair of non-neighboring contacts. In this paper we study more general operating conditions of Hall plates with an arbitrary number of contacts. In such hybrid operating modes current sources are connected to a first set of contacts and voltage sources to a second set of contacts. Output voltages are tapped at the first set of contacts and output currents are measured at the second set of contacts. All these output signals are multiplied by coefficients and added up. The purpose of this work is to figure out which operating mode and which Hall plate achieve maximum signal at minimum thermal noise and power dissipation. To this end we develop a theory, which gives the ratio of signal over noise and power as a function of the resistance matrix of Hall plates, of the supply voltages and currents, and of the coefficients. Optimization is done analytically in closed form and numerically for specific examples. The results are: 1) all operating modes have identical noise performance if their parameters are optimized;2) for any Hall plate one can measure its resistance matrix and insert its values into our formulae to obtain the optimum supply currents and coefficients for optimum noise performance.展开更多
Based on a subspace method and a linear approximation method,a convex algorithm is designed to solve a kind of non-convex PDE constrained fractional optimization problem in this paper.This PDE constrained problem is a...Based on a subspace method and a linear approximation method,a convex algorithm is designed to solve a kind of non-convex PDE constrained fractional optimization problem in this paper.This PDE constrained problem is an infinitedimensional Hermitian eigenvalue optimization problem with non-convex and low regularity.Usually,such a continuous optimization problem can be transformed into a large-scale discrete optimization problem by using the finite element methods.We use a subspace technique to reduce the scale of discrete problem,which is really effective to deal with the large-scale problem.To overcome the difficulties caused by the low regularity and non-convexity,we creatively introduce several new artificial variables to transform the non-convex problem into a convex linear semidefinite programming.By introducing linear approximation vectors,this linear semidefinite programming can be approximated by a very simple linear relaxation problem.Moreover,we theoretically prove this approximation.Our proposed algorithm is used to optimize the photonic band gaps of two-dimensional Gallium Arsenide-based photonic crystals as an application.The results of numerical examples show the effectiveness of our proposed algorithm,while they also provide several optimized photonic crystal structures with a desired wide-band-gap.In addition,our proposed algorithm provides a technical way for solving a kind of PDE constrained fractional optimization problems with a generalized eigenvalue constraint.展开更多
Motivated by the fact that not all nonconvex optimization problems are difficult to solve,we survey in this paper three widely used ways to reveal the hidden convex structure for different classes of nonconvex optimiz...Motivated by the fact that not all nonconvex optimization problems are difficult to solve,we survey in this paper three widely used ways to reveal the hidden convex structure for different classes of nonconvex optimization problems.Finally,ten open problems are raised.展开更多
文摘First, a class of higher order exponential type hybrid (α,β, γ, η, p, h(.,.), κ(., .), w(.,., .), ω(.,.,.), θ)-invexities is introduced, second, some parametrically sufficient efficiency conditions based on the higher order exponential type hybrid invexities are established, and finally some parametrically sufficient efficiency results under the higher order exponential type hybrid (a,β, γ, ρ, h(.,.), k(.,-), w(-,., .), w(.,., .), 0)-invexities are investigated to the context of solving semiinfinite multiobjective fractional programming problems. The notions of the higher order exponential type hybrid (a, β, γ η, p, h(., .), n(., .), w(-,.,-), ω(.,.,.), 0)-invexities encompass most of the generalized invexities in the literature. To the best of our knowledge, the results on semiinfinite multiobjective fractional programming problems established in this communication are new and application-oriented toward multitime multi- objectve problems as well as multiobiective control problems.
基金National Natural Science Foundation of China(No.11071110)
文摘A new concept of(Φ,ρ,α)-V-invexity for differentiable vector-valued functions is introduced,which is a generalization of differentiable scalar-valued(Φ,ρ)-invexity.Based upon the(Φ,ρ,α)-V-invex functions,sufficient optimality conditions and MondWeir type dual theorems are derived for a class of nondifferentiable multiobjective fractional programming problems in which every component of the objective function and each constraint function contain a term involving the support function of a compact convex set.
基金Supported by Chongqing Key Lab. of Operations Research and System Engineering
文摘This paper studies a class of multiobjective generalized fractional programming problems, where the numerators of objective functions are the sum of differentiable function and convex function, while the denominators are the difference of differentiable function and convex function. Under the assumption of Calmness Constraint Qualification the Kuhn-Tucker type necessary conditions for efficient solution are given, and the Kuhn-Tucker type sufficient conditions for efficient solution are presented under the assumptions of (F, α, ρ, d)-V-convexity. Subsequently, the optimality conditions for two kinds of duality models are formulated and duality theorems are proved.
文摘In this paper, two duality results are established under generalized ρ-convexity conditions for a class of multiobjective fractional programmign involvign differentiable n-sten functions.
基金supported by the National Natural Science Foundation of China(Grant 11961001)the construction project of first-class subjects in Ningxia Higher Education(Grant NXYLXK2017B09)by the major proprietary funded project of North Minzu University(Grant ZDZX201901).
文摘The mixed-integer quadratically constrained quadratic fractional programming(MIQCQFP)problem often appears in various fields such as engineering practice,management science and network communication.However,most of the solutions to such problems are often designed for their unique circumstances.This paper puts forward a new global optimization algorithm for solving the problem MIQCQFP.We first convert the MIQCQFP into an equivalent generalized bilinear fractional programming(EIGBFP)problem with integer variables.Secondly,we linearly underestimate and linearly overestimate the quadratic functions in the numerator and the denominator respectively,and then give a linear fractional relaxation technique for EIGBFP on the basis of non-negative numerator.After that,combining rectangular adjustment-segmentation technique and midpointsampling strategy with the branch-and-bound procedure,an efficient algorithm for solving MIQCQFP globally is proposed.Finally,a series of test problems are given to illustrate the effectiveness,feasibility and other performance of this algorithm.
基金supported by Natural Science Foundation of China(Nos.11861002 and 12171601)the Key Project of North Minzu University(No.ZDZX201804)+1 种基金the Construction Project of First-Class Disciplines in Ningxia Higher Education(NXYLXK2017B09)the Postgraduate Innovation Project of North Minzu Universit(No.YCX21157)..
文摘This paper aims at studying optimality conditions of robust weak efficient solutions for a nonsmooth uncertain multi-objective fractional programming problem(NUMFP).The concepts of two types of generalized convex function pairs,called type-I functions and pseudo-quasi-type-I functions,are introduced in this paper for(NUMFP).Under the assumption that(NUMFP)satisfies the robust constraint qualification with respect to Clarke subdifferential,necessary optimality conditions of the robust weak efficient solution are given.Sufficient optimality conditions are obtained under pseudo-quasi-type-I generalized convexity assumption.Furthermore,we introduce the concept of robust weak saddle points to(NUMFP),and prove two theorems about robust weak saddle points.The main results in the present paper are verified by concrete examples.
基金the National Natural Science Foundation of China(Nos.11871196,12071133 and 12071112)the China Postdoctoral Science Foundation(No.2017M622340)+1 种基金the Key Scientific and Technological Research Projects of Henan Province(Nos.202102210147 and 192102210114)the Science and Technology Climbing Program of Henan Institute of Science and Technology(No.2018JY01).
文摘This paper presents an efficient algorithm for globally solving a generalized linear fractional programming problem.For establishing this algorithm,we firstly construct a two-level linear relaxation method,and by utilizing the method,we can convert the initial generalized linear fractional programming problem and its subproblems into a series of linear programming relaxation problems.Based on the branch-and-bound framework and linear programming relaxation problems,a branch-and-bound algorithm is presented for globally solving the generalized linear fractional programming problem,and the computational complexity of the algorithm is given.Finally,numerical experimental results demonstrate the feasibility and efficiency of the proposed algorithm.
文摘A semi-infinite programming problem is a mathematical programming problem with a finite number of variables and infinitely many constraints. Duality theories and generalized convexity concepts are important research topics in mathematical programming. In this paper, we discuss a fairly large number of paramet- ric duality results under various generalized (η,ρ)-invexity assumptions for a semi-infinite minmax fractional programming problem.
基金National Natural Science Foundation of China(51479032,51579044)Yangtze River Scholars in Universities of Heilongjiang Province and Water Conservancy Science and Technology Project of Heilongjiang Province(201318,201503)The Outstanding Youth Fund of Heilongjiang Province(JC201402).
文摘For optimizing the water-use structure and increasing plantation benefit of unit water consumption,a multi-objective model for water resources utilization was established based on fractional programming(FP).Meanwhile,considering the stochasticity of water availability in the study area,the impact of the risk factor(λ)from a quantitative and qualitative perspective was analyzed.The chance-constrained programming(CCP)and conditional value-at-risk(CVaR)models were introduced into five important major grain production areas in Sanjiang Plain,and the crop planting structure under this condition was optimized.The results showed that,after optimization,overall benefit of cultivation increased from 42.07 billion Yuan to 42.47 billion Yuan,water consumption decreased from 15.90 billion m3 to 11.95 billion m3,the plantation benefit of unit water consumption increased from 2.65 Yuan/m3 to 3.55 Yuan/m3.Furthermore,the index of water consumption,benefit of cultivation and plantation benefit of unit water consumption showed an increasing trend with the increase of violation likelihood.However,through the quantification ofλfrom an economic perspective,the increasing ofλcould not enhance plantation benefit of unit water consumption significantly.
文摘In this paper, we discuss a large number of sets of global parametric sufficient optimality conditions under various generalized (η,ρ)-invexity assumptions for a semi-infinite minmax fractional programming problem.
文摘In this paper, we present several parametric duality results under various generalized (a,v,p)-V- invexity assumptions for a semiinfinite multiobjective fractional programming problem.
文摘Abstract In this paper, we discuss numerous sets of global parametric sufficient efficiency conditions under various generalized (a,n, p)-V-invexity assumptions for a semiinfinite multiobjective fractional programming problem.
基金supported by the National Science Foundation of P.R.China (No.61701064)the Chongqing Natural Science Foundation (cstc2019jcyj-msxmX0264).
文摘In Non-Orthogonal Multiple Access(NOMA),the best way to fully exploit the benefits of the system is the efficient resource allocation.For the NOMA power domain,the allocation of power and spectrum require solving the mixed-integer nonlinear programming NP-hard problem.In this paper,we investigate user scheduling and power allocation in Multi-Cell Multi-Carrier NOMA(MCMC-NOMA)networks.To achieve that,we consider Weighted Sum Rate Maximization(WSRM)and Weighted Sum Energy Efficiency Maximization(WSEEM)problems.First,we tackle the problem of user scheduling for fixed power using Fractional Programming(FP),the Lagrange dual method,and the decomposition method.Then,we consider Successive Pseudo-Convex Approximation(SPCA)to deal with the WSRM problem.Finally,for the WSEEM problem,SPCA is utilized to convert the problem into separable scalar problems,which can be parallelly solved.Thus,the Dinkelbach algorithm and constraints relaxation are used to characterize the closed-form solution for power allocation.Extensive simulations have been implemented to show the efficiency of the proposed framework and its superiority over other existing schemes.
基金supported in part by the National Natural Science Foundation of China under Grants 61971126 and 61921004ZTE CorporationState Key Laboratory of Mobile Network and Mobile Multimedia Technology.
文摘In this paper,we investigate the reconfigurable intelligent surface(RIS)-enabled multiple-input-single-output orthogonal frequency division multiplexing(MISO-OFDM)system under frequency-selective channels,and propose a low-complexity alternating optimization(AO)based joint beamforming and RIS phase shifts optimization algorithm to maximize the achievable rate.First,with fixed RIS phase shifts,we devise the optimal closedform transmit beamforming vectors corresponding to different subcarriers.Then,with given active beamforming vectors,near-optimal RIS reflection coefficients can be determined efficiently leveraging fractional programming(FP)combined with manifold optimization(MO)or majorization-minimization(MM)framework.Additionally,we also propose a heuristic RIS phase shifts design approach based on the sum of subcarrier gain maximization(SSGM)criterion requiring lower complexity.Numerical results indicate that the proposed MO/MM algorithm can achieve almost the same rate as the upper bound achieved by the semidefinite relaxation(SDR)algorithm,and the proposed SSGM based scheme is only slightly inferior to the upper bound while has much lower complexity.These results demonstrate the effectiveness of the proposed algorithms.
基金supported by the National Natural Science Foundation of China (No. 61671252)
文摘In this paper, proportional fairness(PF)-based energy-efficient power allocation is studied for multiple-input multiple-output(MIMO) non-orthogonal multiple access(NOMA) systems. In our schemes, statistical channel state information(CSI) is utilized for perfect CSI is impossible to achieve in practice. PF is used to balance the transmission efficiency and user fairness. Energy efficiency(EE) is formulated under basic data rate requirements and maximum transmitting power constraints. Due to the non-convex nature of EE, a two-step algorithm is proposed to obtain sub-optimal solution with a low complexity. Firstly, power allocation is determined by golden section search for fixed power. Secondly total transmitting power is determined by fractional programming method in the feasible regions. Compared to the performance of MIMO-NOMA without PF constraint, fairness is obtained at expense of decreasing of EE.
基金supported in part by the Natural Science Foundation of China under Grant U19B2025,Grant 61725103,Grant 61701363,Grant 61931005,and Grant 62001347.
文摘The efficient antenna scheduling strategy for data relay satellites(DRSs)is essential to optimize the throughput or delay of the satellite data relay network.However,these two objectives conflict with each other since the user satellites(USs)with higher priorities take up more transmission time of DRSs’antennas for greater throughput but the USs storing more packets cause a severer waiting delay to the whole network.To balance the conflicting metrics for meeting the delay-throughput integrated requirements,we formulate the antenna scheduling as a stochastic non-convex fractional programming,which is challenging to be solved.For the tractability,we equivalently transform the fractional programming to a parametric problem and implement the Lyapunov drift to guarantee the constraint of mean rate stability.By proposing a delay and throughput tradeoff based antenna scheduling algorithm,we further transform the parametric problem to a solvable weight matching problem.Simulation results reveal the feasible region of the preference control parameter for integrated QoS cases and its variation relationship with network delay and throughput.
基金supported by the National Natural Science Foundation of China(61371188)the Research Fund for the Doctoral Program of Higher Education(20130131110029)+2 种基金the Open Fund of State Key Laboratory of Integrated Services Networks(ISN14-03)the China Postdoctoral Science Foundation(2014M560553)the Special Funds for Postdoctoral Innovative Projects of Shandong Province(201401013)
文摘The energy efficiency(EE) for the full-duplex massive multi-input multi-output(MIMO) system is investigated. Given the transmit powers of both the uplink and the downlink, the closed-form solutions of the optimal number of antennas and the maximum EE are achieved in the high regime of the signal-to-noise ratio(SNR). It is shown that the optimal number of antennas and the maximum EE gets larger with the increase in user numbers. To further improve the EE, an optimization algorithm with low complexity is proposed to jointly determine the number of antennas and the transmit powers of both the uplink and the downlink. It is shown that, the proposed algorithm can achieve the system performance very close to the exhaustive search.
文摘If Hall plates are used as magnetic field sensors they are usually powered up by a current source connected to a pair of non-neighboring contacts. The output voltage is tapped at another pair of non-neighboring contacts. In this paper we study more general operating conditions of Hall plates with an arbitrary number of contacts. In such hybrid operating modes current sources are connected to a first set of contacts and voltage sources to a second set of contacts. Output voltages are tapped at the first set of contacts and output currents are measured at the second set of contacts. All these output signals are multiplied by coefficients and added up. The purpose of this work is to figure out which operating mode and which Hall plate achieve maximum signal at minimum thermal noise and power dissipation. To this end we develop a theory, which gives the ratio of signal over noise and power as a function of the resistance matrix of Hall plates, of the supply voltages and currents, and of the coefficients. Optimization is done analytically in closed form and numerically for specific examples. The results are: 1) all operating modes have identical noise performance if their parameters are optimized;2) for any Hall plate one can measure its resistance matrix and insert its values into our formulae to obtain the optimum supply currents and coefficients for optimum noise performance.
基金supported by National Natural Science Foundation of China(Grant Nos.12171052 and 11871115)BUPT Excellent Ph.D.Students Foundation(Grant No.CX2021320).
文摘Based on a subspace method and a linear approximation method,a convex algorithm is designed to solve a kind of non-convex PDE constrained fractional optimization problem in this paper.This PDE constrained problem is an infinitedimensional Hermitian eigenvalue optimization problem with non-convex and low regularity.Usually,such a continuous optimization problem can be transformed into a large-scale discrete optimization problem by using the finite element methods.We use a subspace technique to reduce the scale of discrete problem,which is really effective to deal with the large-scale problem.To overcome the difficulties caused by the low regularity and non-convexity,we creatively introduce several new artificial variables to transform the non-convex problem into a convex linear semidefinite programming.By introducing linear approximation vectors,this linear semidefinite programming can be approximated by a very simple linear relaxation problem.Moreover,we theoretically prove this approximation.Our proposed algorithm is used to optimize the photonic band gaps of two-dimensional Gallium Arsenide-based photonic crystals as an application.The results of numerical examples show the effectiveness of our proposed algorithm,while they also provide several optimized photonic crystal structures with a desired wide-band-gap.In addition,our proposed algorithm provides a technical way for solving a kind of PDE constrained fractional optimization problems with a generalized eigenvalue constraint.
基金This research was supported by the National Natural Science Foundation of China(Nos.11822103,11571029)Natural Science Foundation of Beijing(No.Z180005).
文摘Motivated by the fact that not all nonconvex optimization problems are difficult to solve,we survey in this paper three widely used ways to reveal the hidden convex structure for different classes of nonconvex optimization problems.Finally,ten open problems are raised.