In this paper, we establish a second-order sufficient condition for constrained optimization problems of a class of so called t-stable functions in terms of the first-order and the second-order Dini type directional d...In this paper, we establish a second-order sufficient condition for constrained optimization problems of a class of so called t-stable functions in terms of the first-order and the second-order Dini type directional derivatives. The result extends the corresponding result of [D. Bednarik and K. Pastor, Math. Program. Ser. A, 113(2008), 283-298] to constrained optimization problems.展开更多
In this paper, a new derivative free trust region method is developed based on the conic interpolation model for the unconstrained optimization. The conic interpolation model is built by means of the quadratic model f...In this paper, a new derivative free trust region method is developed based on the conic interpolation model for the unconstrained optimization. The conic interpolation model is built by means of the quadratic model function, the collinear scaling formula, quadratic approximation and interpolation. All the parameters in this model are determined by objective function interpolation condition. A new derivative free method is developed based upon this model and the global convergence of this new method is proved without any information on gradient.展开更多
Trust region methods are powerful and effective optimization methods. The conic model method is a new type of method with more information available at each iteration than standard quadratic-based methods. The adva...Trust region methods are powerful and effective optimization methods. The conic model method is a new type of method with more information available at each iteration than standard quadratic-based methods. The advantages of the above two methods can be combined to form a more powerful method for constrained optimization. The trust region subproblem of our method is to minimize a conic function subject to the linearized constraints and trust region bound. At the same time, the new algorithm still possesses robust global properties. The global convergence of the new algorithm under standard conditions is established.展开更多
A complex autonomous inventory coupled system is considered. It can take, for example, the form of a network of chemical or biochemical reactors, where the inventory interactions perform the recycling of by-products b...A complex autonomous inventory coupled system is considered. It can take, for example, the form of a network of chemical or biochemical reactors, where the inventory interactions perform the recycling of by-products between the subsystems. Because of the flexible subsystems interactions, each of them can be operated with their own periods utilizing advantageously their dynamic properties. A multifrequency second-order test generalizing the p-test for single systems is described. It can be used to decide which kind of the operation (the static one, the periodic one or the multiperiodic one) will intensify the productivity of a complex system. An illustrative example of the multiperiodic optimization of a complex chemical production system is presented.展开更多
The traditional guidance law only guarantees the accuracy of attacking a target. However, the look angle and acceleration constraints are indispensable in applications. A new adaptive three-dimensional proportional na...The traditional guidance law only guarantees the accuracy of attacking a target. However, the look angle and acceleration constraints are indispensable in applications. A new adaptive three-dimensional proportional navigation(PN) guidance law is proposed based on convex optimization. Decomposition of the three-dimensional space is carried out to establish threedimensional kinematic engagements. The constraints and the performance index are disposed by using the convex optimization method. PN guidance gains can be obtained by solving the optimization problem. This solution is more rapid and programmatic than the traditional method and provides a foundation for future online guidance methods, which is of great value for engineering applications.展开更多
Optimization algorithms are applied to resolve the second-order pileup(SOP)issue from high counting rates occurring in digital alpha spectroscopy.These are antlion optimizer(ALO)and particle swarm optimization(PSO)alg...Optimization algorithms are applied to resolve the second-order pileup(SOP)issue from high counting rates occurring in digital alpha spectroscopy.These are antlion optimizer(ALO)and particle swarm optimization(PSO)algorithms.Both optimization algorithms are coupled to one of the three proposed peak finder algorithms.Three custom time-domain algorithms are proposed for retrieving SOP peaks,namely peak seek,slope tangent,and fast array algorithms.In addition,an average combinational algorithm is applied.The time occurrence of the retrieved peaks is tested for an elimination of illusive pulses.Conventional methods are inaccurate and timeconsuming.ALO and PSO optimizations are used for the localization of retrieved peaks.Optimum cost values that achieve the best fitness values are demonstrated.Thus,the optimum positions of the detected peak heights are achieved.Evaluation metrics of the optimized algorithms and their influences on the retrieved peaks parameters are established.Comparisons among such algorithms are investigated,and the algorithms are inspected in terms of their computational time and average error.The peak seek algorithm achieves the lowest average computational error for pulse parameters(amplitude and position).However,the fast array algorithm introduces the largest average error for pulse parameters.In addition,the peak seek algorithm coupled with an ALO or PSO algorithm is observed to realize a better performance in terms of the optimum cost and computational time.By contrast,the performance of the peak seek recovery algorithm is improved using the PSO.Furthermore,the computational time of the peak optimization using the PSO is much better than that of the ALO algorithm.As a final conclusion,the accuracy of the peaks detected by the PSO surpasses that for the peaks detected by the ALO.The implemented peak retrieval algorithms are validated through a comparison with experimental results from previous studies.The proposed algorithms achieve a notable precision for compensation of the SOP peaks within the alpha ray spectroscopy at a high counting rate.展开更多
Owing to the multipath effect, the source localization in shallow water has been an area of active interest. However, most methods for source localization in shallow water are sensitive to the assumed model of the und...Owing to the multipath effect, the source localization in shallow water has been an area of active interest. However, most methods for source localization in shallow water are sensitive to the assumed model of the underwater environment and have poor robustness against the underwater channel uncertainty, which limit their further application in practical engineering. In this paper, a new method of source localization in shallow water, based on vector optimization concept, is described, which is highly robust against environmental factors affecting the localization, such as the channel depth, the bottom reflection coefficients, and so on. Through constructing the uncertainty set of the source vector errors and extracting the multi-path sound rays from the sea surface and bottom, the proposed method can accurately localize one or more sources in shallow water dominated by multipath propagation. It turns out that the natural formulation of our approach involves minimization of two quadratic functions subject to infinitely many nonconvex quadratic constraints. It shows that this problem (originally intractable) can be reformulated in a convex form as the so-called second-order cone program (SOCP) and solved efficiently by using the well-established interior point method, such as the sottware tool, SeDuMi. Computer simulations show better performance of the proposed method as compared with existing algorithms and establish a theoretical foundation for the practical engineering application.展开更多
A vu-decomposition method for solving a second-order cone problem is presented in this paper. It is first transformed into a nonlinear programming problem. Then, the structure of the Clarke subdifferential correspondi...A vu-decomposition method for solving a second-order cone problem is presented in this paper. It is first transformed into a nonlinear programming problem. Then, the structure of the Clarke subdifferential corresponding to the penalty function and some results of itsvu-decomposition are given. Under a certain condition, a twice continuously differentiable trajectory is computed to produce a second-order expansion of the objective function. A conceptual algorithm for solving this problem with a superlinear convergence rate is given.展开更多
In this paper, we approach the problem of obtaining approximate solution of second-order initial value problems by converting it to an optimization problem. It is assumed that the solution can be approximated by a pol...In this paper, we approach the problem of obtaining approximate solution of second-order initial value problems by converting it to an optimization problem. It is assumed that the solution can be approximated by a polynomial. The coefficients of the polynomial are then optimized using simulated annealing technique. Numerical examples with good results show the accuracy of the proposed approach compared with some existing methods.展开更多
The geometric shape of the wheel tread is mathematically expressed,and geometric parameters affecting the shape of the wheel were extracted as design variables.The vehicle dynamics simulation model was established bas...The geometric shape of the wheel tread is mathematically expressed,and geometric parameters affecting the shape of the wheel were extracted as design variables.The vehicle dynamics simulation model was established based on the vehicle suspension parameters and track conditions of the actual operation,and the comprehensive dynamic parameters of the vehicle were taken as the design objectives.The matching performance of the wheel equivalent conicity with the vehicle and track parameters was discussed,and the best equivalent conicity was determined as the constraint condition of the optimization problem;a numerical calculation program is written to solve the optimization model based on a multi-population genetic algorithm.The results show that the algorithm has a fast calculation speed and good convergence.Compared with the LM profile,the two optimized profiles effectively reduce the wheelset acceleration and improve the lateral stability of the bogie and vehicle stability during straight running.Due to the optimized profile increases the equivalent conicity under larger lateral displacement of the wheelset,the lateral wheel-rail force,derailment coefficient,wheel load reduction rate,and wear index are reduced when the train passes through the curve line.This paper provides a feasible way to ensure the speed-up operation of a freight train.展开更多
In this paper,we establish a second-order necessary conditions for stochastic optimal control for jump diffusions.The controlled system is described by a stochastic differential systems driven by Poisson random measur...In this paper,we establish a second-order necessary conditions for stochastic optimal control for jump diffusions.The controlled system is described by a stochastic differential systems driven by Poisson random measure and an independent Brownian motion.The control domain is assumed to be convex.Pointwise second-order maximum principle for controlled jump diffusion in terms of the martingale with respect to the time variable is proved.The proof of the main result is based on variational approach using the stochastic calculus of jump diffusions and some estimates on the state processes.展开更多
This paper proposes an optimal day-ahead opti-mization schedule for gas-electric integrated energy system(IES)considering the bi-directional energy flow.The hourly topology of electric power system(EPS),natural gas sy...This paper proposes an optimal day-ahead opti-mization schedule for gas-electric integrated energy system(IES)considering the bi-directional energy flow.The hourly topology of electric power system(EPS),natural gas system(NGS),energy hubs(EH)integrated power to gas(P2G)unit,are modeled to minimize the day-ahead operation cost of IES.Then,a second-order cone programming(SOCP)method is utilized to solve the optimization problem,which is actually a mixed integer nonconvex and nonlinear programming issue.Besides,cutting planes are added to ensure the exactness of the global optimal solution.Finally,simulation results demonstrate that the proposed optimization schedule can provide a safe,effective and economical day-ahead scheduling scheme for gas-electric IES.展开更多
A class of polynomial primal-dual interior-point algorithms for second-order cone optimization based on a new parametric kernel function, with parameters p and q, is presented. Its growth term is between linear and qu...A class of polynomial primal-dual interior-point algorithms for second-order cone optimization based on a new parametric kernel function, with parameters p and q, is presented. Its growth term is between linear and quadratic. Some new tools for the analysis of the algorithms are proposed. The complexity bounds of O(√Nlog N log N/ε) for large-update methods and O(√Nlog N/ε) for smallupdate methods match the best known complexity bounds obtained for these methods. Numerical tests demonstrate the behavior of the algorithms for different results of the parameters p and q.展开更多
This paper addresses the distributed adaptive optimization problem over second-order multi-agent networks(MANs)with nonuniform gradient gains.A general convex function consisting of a sum of local differentiable conve...This paper addresses the distributed adaptive optimization problem over second-order multi-agent networks(MANs)with nonuniform gradient gains.A general convex function consisting of a sum of local differentiable convex functions is chosen as the team objective function.First,based on the local information of each agent’s neighborhood,a novel distributed adaptive optimization algorithm with nonuniform gradient gains is designed,where these gains only have relations with agents’own states.And then,the original closed-loop system is changed into an equivalent one by taking a coordination transformation.Moreover,it is proved that the states including positions and velocities of all agents are bounded by constructing a Lyapunov function provided that the initial values are given.By the theory of Lyapunov stability,it is shown that all agents can finally reach an agreement and their position states converge to the optimal solution of the team objective function asymptotically.Finally,the effectiveness of the obtained theoretical results is demonstrated by several simulation examples.展开更多
This paper is devoted to developing first-order necessary,second-order necessary,and second-order sufficient optimality conditions for a multiobjective optimization problem whose order is induced by a finite product o...This paper is devoted to developing first-order necessary,second-order necessary,and second-order sufficient optimality conditions for a multiobjective optimization problem whose order is induced by a finite product of second-order cones(here named as Q-multiobjective optimization problem).For an abstract-constrained Q-multiobjective optimization problem,we derive two basic necessary optimality theorems for weak efficient solutions and a second-order sufficient optimality theorem for efficient solutions.For Q-multiobjective optimization problem with explicit constraints,we demonstrate first-order and second-order necessary optimality conditions under Robinson constraint qualification as well as second-order sufficient optimality conditions under upper second-order regularity for the explicit constraints.As applications,we obtain optimality conditions for polyhedral conic,second-order conic,and semi-definite conic Q-multiobjective optimization problems.展开更多
In this paper, we introduce the concept of second-order compound contingent epiderivative for set-valued maps and discuss its relationship to the second-order contingent epiderivative. Simultaneously, we also investig...In this paper, we introduce the concept of second-order compound contingent epiderivative for set-valued maps and discuss its relationship to the second-order contingent epiderivative. Simultaneously, we also investigate some special properties of the second-order compound contingent epiderivative. By virtue of the second-order compound contingent epiderivative, we establish some unified second-order sufficient and necessary optimality conditions for set-valued optimization problems. All results in this paper generalize the corresponding results in the literature.展开更多
A Class of Collinear Scaling Algorithms for Unconstrained Optimization. An appealing approach to the solution of nonlinear optimization problems based on conic models of the objective function has been in troduced by ...A Class of Collinear Scaling Algorithms for Unconstrained Optimization. An appealing approach to the solution of nonlinear optimization problems based on conic models of the objective function has been in troduced by Davidon (1980). It leads to a broad class of algorithms which can be considered to generalize the existing quasi-Newton methods. One particular member of this class has been deeply discussed by Sorensen (1980), who has proved some interesting theoretical properties. In this paper, we generalize Sorensen’s technique to Spedicato three-parameter family of variable-metric updates. Furthermore, we point out that the collinear scaling three- parameter family is essentially equivalent to the Spedicato three-parameter family. In addition, numerical expriments have been carried out to compare some colliner scaling algorithms with a straightforward implementation of the BFGS quasi-Newton method.展开更多
This paper studies the nonhomogeneous quadratic programming problem over a second-order cone with linear equality constraints.When the feasible region is bounded,we show that an optimal solution of the problem can be ...This paper studies the nonhomogeneous quadratic programming problem over a second-order cone with linear equality constraints.When the feasible region is bounded,we show that an optimal solution of the problem can be found in polynomial time.When the feasible region is unbounded,a semidefinite programming(SDP)reformulation is constructed to find the optimal objective value of the original problem in polynomial time.In addition,we provide two sufficient conditions,under which,if the optimal objective value is finite,we show the optimal solution of SDP reformulation can be decomposed into the original space to generate an optimal solution of the original problem in polynomial time.Otherwise,a recession direction can be identified in polynomial time.Numerical examples are included to illustrate the effectiveness of the proposed approach.展开更多
基金The Graduate Students Innovate Scientific Research Program (YJSCX2008-158HLJ) of Heilongjiang Provincesupported by the Distinguished Young Scholar Foundation (JC200707) of Heilongjiang Province of China
文摘In this paper, we establish a second-order sufficient condition for constrained optimization problems of a class of so called t-stable functions in terms of the first-order and the second-order Dini type directional derivatives. The result extends the corresponding result of [D. Bednarik and K. Pastor, Math. Program. Ser. A, 113(2008), 283-298] to constrained optimization problems.
基金This work was supported by the National Natural Science Foundation of China(10071037)
文摘In this paper, a new derivative free trust region method is developed based on the conic interpolation model for the unconstrained optimization. The conic interpolation model is built by means of the quadratic model function, the collinear scaling formula, quadratic approximation and interpolation. All the parameters in this model are determined by objective function interpolation condition. A new derivative free method is developed based upon this model and the global convergence of this new method is proved without any information on gradient.
文摘Trust region methods are powerful and effective optimization methods. The conic model method is a new type of method with more information available at each iteration than standard quadratic-based methods. The advantages of the above two methods can be combined to form a more powerful method for constrained optimization. The trust region subproblem of our method is to minimize a conic function subject to the linearized constraints and trust region bound. At the same time, the new algorithm still possesses robust global properties. The global convergence of the new algorithm under standard conditions is established.
文摘A complex autonomous inventory coupled system is considered. It can take, for example, the form of a network of chemical or biochemical reactors, where the inventory interactions perform the recycling of by-products between the subsystems. Because of the flexible subsystems interactions, each of them can be operated with their own periods utilizing advantageously their dynamic properties. A multifrequency second-order test generalizing the p-test for single systems is described. It can be used to decide which kind of the operation (the static one, the periodic one or the multiperiodic one) will intensify the productivity of a complex system. An illustrative example of the multiperiodic optimization of a complex chemical production system is presented.
基金supported by the National Natural Science Foundation of China(61803357)。
文摘The traditional guidance law only guarantees the accuracy of attacking a target. However, the look angle and acceleration constraints are indispensable in applications. A new adaptive three-dimensional proportional navigation(PN) guidance law is proposed based on convex optimization. Decomposition of the three-dimensional space is carried out to establish threedimensional kinematic engagements. The constraints and the performance index are disposed by using the convex optimization method. PN guidance gains can be obtained by solving the optimization problem. This solution is more rapid and programmatic than the traditional method and provides a foundation for future online guidance methods, which is of great value for engineering applications.
文摘Optimization algorithms are applied to resolve the second-order pileup(SOP)issue from high counting rates occurring in digital alpha spectroscopy.These are antlion optimizer(ALO)and particle swarm optimization(PSO)algorithms.Both optimization algorithms are coupled to one of the three proposed peak finder algorithms.Three custom time-domain algorithms are proposed for retrieving SOP peaks,namely peak seek,slope tangent,and fast array algorithms.In addition,an average combinational algorithm is applied.The time occurrence of the retrieved peaks is tested for an elimination of illusive pulses.Conventional methods are inaccurate and timeconsuming.ALO and PSO optimizations are used for the localization of retrieved peaks.Optimum cost values that achieve the best fitness values are demonstrated.Thus,the optimum positions of the detected peak heights are achieved.Evaluation metrics of the optimized algorithms and their influences on the retrieved peaks parameters are established.Comparisons among such algorithms are investigated,and the algorithms are inspected in terms of their computational time and average error.The peak seek algorithm achieves the lowest average computational error for pulse parameters(amplitude and position).However,the fast array algorithm introduces the largest average error for pulse parameters.In addition,the peak seek algorithm coupled with an ALO or PSO algorithm is observed to realize a better performance in terms of the optimum cost and computational time.By contrast,the performance of the peak seek recovery algorithm is improved using the PSO.Furthermore,the computational time of the peak optimization using the PSO is much better than that of the ALO algorithm.As a final conclusion,the accuracy of the peaks detected by the PSO surpasses that for the peaks detected by the ALO.The implemented peak retrieval algorithms are validated through a comparison with experimental results from previous studies.The proposed algorithms achieve a notable precision for compensation of the SOP peaks within the alpha ray spectroscopy at a high counting rate.
基金This Project supported by the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No.20122304120011)the Fundamental Research Funds for the Central Universities of Ministry of Education of China (Grant No.HEUCFR1119)
文摘Owing to the multipath effect, the source localization in shallow water has been an area of active interest. However, most methods for source localization in shallow water are sensitive to the assumed model of the underwater environment and have poor robustness against the underwater channel uncertainty, which limit their further application in practical engineering. In this paper, a new method of source localization in shallow water, based on vector optimization concept, is described, which is highly robust against environmental factors affecting the localization, such as the channel depth, the bottom reflection coefficients, and so on. Through constructing the uncertainty set of the source vector errors and extracting the multi-path sound rays from the sea surface and bottom, the proposed method can accurately localize one or more sources in shallow water dominated by multipath propagation. It turns out that the natural formulation of our approach involves minimization of two quadratic functions subject to infinitely many nonconvex quadratic constraints. It shows that this problem (originally intractable) can be reformulated in a convex form as the so-called second-order cone program (SOCP) and solved efficiently by using the well-established interior point method, such as the sottware tool, SeDuMi. Computer simulations show better performance of the proposed method as compared with existing algorithms and establish a theoretical foundation for the practical engineering application.
基金Project supported by the National Natural Science Foundation of China (No. 10771026)the Foundation of Dalian University of Technology (Nos. MXDUT73008 and MXDUT98009)
文摘A vu-decomposition method for solving a second-order cone problem is presented in this paper. It is first transformed into a nonlinear programming problem. Then, the structure of the Clarke subdifferential corresponding to the penalty function and some results of itsvu-decomposition are given. Under a certain condition, a twice continuously differentiable trajectory is computed to produce a second-order expansion of the objective function. A conceptual algorithm for solving this problem with a superlinear convergence rate is given.
文摘In this paper, we approach the problem of obtaining approximate solution of second-order initial value problems by converting it to an optimization problem. It is assumed that the solution can be approximated by a polynomial. The coefficients of the polynomial are then optimized using simulated annealing technique. Numerical examples with good results show the accuracy of the proposed approach compared with some existing methods.
基金The present work was supported by Sichuan Science and Technology Program(2020YJ0308 and 2021YJ0026).
文摘The geometric shape of the wheel tread is mathematically expressed,and geometric parameters affecting the shape of the wheel were extracted as design variables.The vehicle dynamics simulation model was established based on the vehicle suspension parameters and track conditions of the actual operation,and the comprehensive dynamic parameters of the vehicle were taken as the design objectives.The matching performance of the wheel equivalent conicity with the vehicle and track parameters was discussed,and the best equivalent conicity was determined as the constraint condition of the optimization problem;a numerical calculation program is written to solve the optimization model based on a multi-population genetic algorithm.The results show that the algorithm has a fast calculation speed and good convergence.Compared with the LM profile,the two optimized profiles effectively reduce the wheelset acceleration and improve the lateral stability of the bogie and vehicle stability during straight running.Due to the optimized profile increases the equivalent conicity under larger lateral displacement of the wheelset,the lateral wheel-rail force,derailment coefficient,wheel load reduction rate,and wear index are reduced when the train passes through the curve line.This paper provides a feasible way to ensure the speed-up operation of a freight train.
文摘In this paper,we establish a second-order necessary conditions for stochastic optimal control for jump diffusions.The controlled system is described by a stochastic differential systems driven by Poisson random measure and an independent Brownian motion.The control domain is assumed to be convex.Pointwise second-order maximum principle for controlled jump diffusion in terms of the martingale with respect to the time variable is proved.The proof of the main result is based on variational approach using the stochastic calculus of jump diffusions and some estimates on the state processes.
基金This work was supported in part by the National Natural Science Foundation of China under Grants 61673161 and 51807134and in part by the program of fundamental research of the Siberian Branch of Russian Academy of Sciences and carried out within the framework of the research project III.17.3.1,Reg.No.AAAA-A17-117030310442-8.
文摘This paper proposes an optimal day-ahead opti-mization schedule for gas-electric integrated energy system(IES)considering the bi-directional energy flow.The hourly topology of electric power system(EPS),natural gas system(NGS),energy hubs(EH)integrated power to gas(P2G)unit,are modeled to minimize the day-ahead operation cost of IES.Then,a second-order cone programming(SOCP)method is utilized to solve the optimization problem,which is actually a mixed integer nonconvex and nonlinear programming issue.Besides,cutting planes are added to ensure the exactness of the global optimal solution.Finally,simulation results demonstrate that the proposed optimization schedule can provide a safe,effective and economical day-ahead scheduling scheme for gas-electric IES.
文摘A class of polynomial primal-dual interior-point algorithms for second-order cone optimization based on a new parametric kernel function, with parameters p and q, is presented. Its growth term is between linear and quadratic. Some new tools for the analysis of the algorithms are proposed. The complexity bounds of O(√Nlog N log N/ε) for large-update methods and O(√Nlog N/ε) for smallupdate methods match the best known complexity bounds obtained for these methods. Numerical tests demonstrate the behavior of the algorithms for different results of the parameters p and q.
基金the National Natural Science Foundation of China under Grant Nos.61973329 and 61772063the Beijing Natural Science Foundation under Grant Nos.Z180005 and 9192008。
文摘This paper addresses the distributed adaptive optimization problem over second-order multi-agent networks(MANs)with nonuniform gradient gains.A general convex function consisting of a sum of local differentiable convex functions is chosen as the team objective function.First,based on the local information of each agent’s neighborhood,a novel distributed adaptive optimization algorithm with nonuniform gradient gains is designed,where these gains only have relations with agents’own states.And then,the original closed-loop system is changed into an equivalent one by taking a coordination transformation.Moreover,it is proved that the states including positions and velocities of all agents are bounded by constructing a Lyapunov function provided that the initial values are given.By the theory of Lyapunov stability,it is shown that all agents can finally reach an agreement and their position states converge to the optimal solution of the team objective function asymptotically.Finally,the effectiveness of the obtained theoretical results is demonstrated by several simulation examples.
基金This work was supported by the National Natural Science Foundation of China(Nos.11571059,11731013 and 91330206).
文摘This paper is devoted to developing first-order necessary,second-order necessary,and second-order sufficient optimality conditions for a multiobjective optimization problem whose order is induced by a finite product of second-order cones(here named as Q-multiobjective optimization problem).For an abstract-constrained Q-multiobjective optimization problem,we derive two basic necessary optimality theorems for weak efficient solutions and a second-order sufficient optimality theorem for efficient solutions.For Q-multiobjective optimization problem with explicit constraints,we demonstrate first-order and second-order necessary optimality conditions under Robinson constraint qualification as well as second-order sufficient optimality conditions under upper second-order regularity for the explicit constraints.As applications,we obtain optimality conditions for polyhedral conic,second-order conic,and semi-definite conic Q-multiobjective optimization problems.
基金Supported in part by the National Natural Science Foundation of China under Grant No.11601437,11526165and 11571055the Scientific Research Fund of Sichuan Provincial Science and Technology Department under Grant No.2015JY0237the Fundamental Research Funds for the Central Universities under Grant No.JBK160129
文摘In this paper, we introduce the concept of second-order compound contingent epiderivative for set-valued maps and discuss its relationship to the second-order contingent epiderivative. Simultaneously, we also investigate some special properties of the second-order compound contingent epiderivative. By virtue of the second-order compound contingent epiderivative, we establish some unified second-order sufficient and necessary optimality conditions for set-valued optimization problems. All results in this paper generalize the corresponding results in the literature.
基金Supported by NNSF of China and NSF of Jiangsu Province
文摘A Class of Collinear Scaling Algorithms for Unconstrained Optimization. An appealing approach to the solution of nonlinear optimization problems based on conic models of the objective function has been in troduced by Davidon (1980). It leads to a broad class of algorithms which can be considered to generalize the existing quasi-Newton methods. One particular member of this class has been deeply discussed by Sorensen (1980), who has proved some interesting theoretical properties. In this paper, we generalize Sorensen’s technique to Spedicato three-parameter family of variable-metric updates. Furthermore, we point out that the collinear scaling three- parameter family is essentially equivalent to the Spedicato three-parameter family. In addition, numerical expriments have been carried out to compare some colliner scaling algorithms with a straightforward implementation of the BFGS quasi-Newton method.
基金Fang was supported by the US National Science Foundation(No.DMI-0553310)Guo,Wang and Xing were supported by the National Natural Science Foundation of China(Nos.11171177 and 11371216)Deng was supported by the Edward P.Fitts Fellowship at North Carolina State University.
文摘This paper studies the nonhomogeneous quadratic programming problem over a second-order cone with linear equality constraints.When the feasible region is bounded,we show that an optimal solution of the problem can be found in polynomial time.When the feasible region is unbounded,a semidefinite programming(SDP)reformulation is constructed to find the optimal objective value of the original problem in polynomial time.In addition,we provide two sufficient conditions,under which,if the optimal objective value is finite,we show the optimal solution of SDP reformulation can be decomposed into the original space to generate an optimal solution of the original problem in polynomial time.Otherwise,a recession direction can be identified in polynomial time.Numerical examples are included to illustrate the effectiveness of the proposed approach.