In order to reduce the intrinsic interference of the filter bank multicarrier-quadrature amplitude modulation(FBMC-QAM)system,a novel filter optimization scheme based on discrete prolate spheroidal sequences(DPSS)is p...In order to reduce the intrinsic interference of the filter bank multicarrier-quadrature amplitude modulation(FBMC-QAM)system,a novel filter optimization scheme based on discrete prolate spheroidal sequences(DPSS)is proposed.Firstly,a prototype filter function based on DPSS is designed,since the eigenvalue can be used as an indicator of the energy concentration of DPSS,so a threshold is set,and the sequence with the most concentrated energy is selected under the threshold,that is,the sequence with the eigenvalue higher than the threshold,and the prototype filter function is rewritten as a weighted sum function of multiple eigenvectors.Under the energy constraints of the filter,the relationship between the eigenvectors and the intrinsic interference function is established,and the function problem is transformed into an optimization problem for the weighted coefficients.Through the interior point method,the most suitable weight is found to obtain the minimum intrinsic interference result.Theoretical analysis and simulation results show that compared with the prototype filters such as Type1 and CaseC,the DPSS filter applying the proposed optimization algorithm can effectively suppress the intrinsic interference of the system and obtain a better bit error rate(BER)performance.展开更多
In this paper, on the basis of the logarithmic barrier function and KKT conditions, we propose a combined homotopy infeasible interior-point method (CHIIP) for convex nonlinear programming problems. For any convex n...In this paper, on the basis of the logarithmic barrier function and KKT conditions, we propose a combined homotopy infeasible interior-point method (CHIIP) for convex nonlinear programming problems. For any convex nonlinear programming, without strict convexity for the logarithmic barrier function, we get different solutions of the convex programming in different cases by CHIIP method.展开更多
A penalized interior point approach for constrained nonlinear programming is examined in this work. To overcome the difficulty of initialization for the interior point method, a problem equivalent to the primal proble...A penalized interior point approach for constrained nonlinear programming is examined in this work. To overcome the difficulty of initialization for the interior point method, a problem equivalent to the primal problem via incorporating an auxiliary variable is constructed. A combined approach of logarithm barrier and quadratic penalty function is proposed to solve the problem. Based on Newton's method, the global convergence of interior point and line search algorithm is proven. Only a finite number of iterations is required to reach an approximate optimal solution. Numerical tests are given to show the effectiveness of the method.展开更多
The element-free Galerkin method is proposed to solve free vibration of rectangular plates with finite interior elastic point supports and elastically restrained edges.Based on the extended Hamilton's principle for t...The element-free Galerkin method is proposed to solve free vibration of rectangular plates with finite interior elastic point supports and elastically restrained edges.Based on the extended Hamilton's principle for the elastic dynamics system,the dimensionless equations of motion of rectangular plates with finite interior elastic point supports and the edge elastically restrained are established using the element-free Galerkin method.Through numerical calculation,curves of the natural frequency of thin plates with three edges simply supported and one edge elastically restrained,and three edges clamped and the other edge elastically restrained versus the spring constant,locations of elastic point support and the elastic stiffness of edge elastically restrained are obtained.Effects of elastic point supports and edge elastically restrained on the free vibration characteristics of the thin plates are analyzed.展开更多
In this paper, we propose a primal-dual interior point method for solving general constrained nonlinear programming problems. To avoid the situation that the algorithm we use may converge to a saddle point or a local ...In this paper, we propose a primal-dual interior point method for solving general constrained nonlinear programming problems. To avoid the situation that the algorithm we use may converge to a saddle point or a local maximum, we utilize a merit function to guide the iterates toward a local minimum. Especially, we add the parameter ε to the Newton system when calculating the decrease directions. The global convergence is achieved by the decrease of a merit function. Furthermore, the numerical results confirm that the algorithm can solve this kind of problems in an efficient way.展开更多
In this paper,we are mainly devoted to solving fixed point problems in more general nonconvex sets via an interior point homotopy method.Under suitable conditions,a constructive proof is given to prove the existence o...In this paper,we are mainly devoted to solving fixed point problems in more general nonconvex sets via an interior point homotopy method.Under suitable conditions,a constructive proof is given to prove the existence of fixed points,which can lead to an implementable globally convergent algorithm.展开更多
The finite-dimensional variational inequality problem (VIP) has been studied extensively in the literature because of its successful applications in many fields such as economics, transportation, regional science and ...The finite-dimensional variational inequality problem (VIP) has been studied extensively in the literature because of its successful applications in many fields such as economics, transportation, regional science and operations research. Barker and Pang[1] have given an excellent survey of theories, methods and applications of VIPs.展开更多
Low-order wavefront error account for a large proportion of wave aberrations.A compensation method for low order aberration of projection lithography objective based on Interior Point Method is presented.Compensation ...Low-order wavefront error account for a large proportion of wave aberrations.A compensation method for low order aberration of projection lithography objective based on Interior Point Method is presented.Compensation model between wavefront error and degree of movable lens freedom is established.Converting over-determined system to underdetermined system,the compensation is solved by Interior Point Method(IPM).The presented method is compared with direct solve the over-determined system.Then,other algorithm GA,EA and PS is compared with IPM.Simulation and experimental results show that the presented compensation method can obtained compensation with less residuals compared with direct solve the over-determined system.Also,the presented compensation method can reduce computation time and obtain results with less residuals compare with AGA,EA and PS.Moreover,after compensation,RMS of wavefront error of the experimental lithography projection objective decrease from 56.05 nm to 17.88 nm.展开更多
This paper proposes an interior-point technique for detecting the nondominated points of multi-objective optimization problems using the direction-based cone method.Cone method decomposes the multi-objective optimizat...This paper proposes an interior-point technique for detecting the nondominated points of multi-objective optimization problems using the direction-based cone method.Cone method decomposes the multi-objective optimization problems into a set of single-objective optimization problems.For this set of problems,parametric perturbed KKT conditions are derived.Subsequently,an interior point technique is developed to solve the parametric perturbed KKT conditions.A differentiable merit function is also proposed whose stationary point satisfies the KKT conditions.Under some mild assumptions,the proposed algorithm is shown to be globally convergent.Numerical results of unconstrained and constrained multi-objective optimization test problems are presented.Also,three performance metrics(modified generational distance,hypervolume,inverted generational distance)are used on some test problems to investigate the efficiency of the proposed algorithm.We also compare the results of the proposed algorithm with the results of some other existing popular methods.展开更多
An interior point of a finite planar point set is a point of the set that is not on the boundary of the convex hull of the set.For any integer fc > 1,let h(k) be the smallest integer such that every set of points i...An interior point of a finite planar point set is a point of the set that is not on the boundary of the convex hull of the set.For any integer fc > 1,let h(k) be the smallest integer such that every set of points in the plane,no three collinear,with at least h(k) interior points,has a subset of points with exactly fc or fc + 1 interior points of P.We prove that h(5) = 11.展开更多
This article establishes several new geometric inequalities, which refer to the lengthes of the edges of a simplex and interior point, height, lateral area, and the circumradius of another simplex.
With the rapid development of the wind generation,uncertainties of random wind and load bring some inevitable impacts on the security of power system. Once the uncertainty causes line power to exceed its limit, line o...With the rapid development of the wind generation,uncertainties of random wind and load bring some inevitable impacts on the security of power system. Once the uncertainty causes line power to exceed its limit, line overload will occur. The paper presents the risk control of transmission line overload for windintegrated power systems. Firstly, a risk control model of line overload is proposed considering the uncertainties of loads,generator outputs and wind powers. The generation cost and security level of system associated with overload can be optimally controlled. Then path following interior point method is employed to carry out the optimal control. Finally the simulation is made on the modified IEEE-30 bus system. Results show that the risk of line overload is effectively reduced through the optimization of control variables.展开更多
In this paper, an unbounded condition is presented, under which we are able to utilize the interior point homotopy method to solve the Brouwer fixed point problem on unbounded sets. Two numerical examples in R3 are pr...In this paper, an unbounded condition is presented, under which we are able to utilize the interior point homotopy method to solve the Brouwer fixed point problem on unbounded sets. Two numerical examples in R3 are presented to illustrate the results in this paper.展开更多
The aim of this paper is to reduce the losses, total generation cost by switching of transmission line and to maintain voltage security under N - 1 contingency conditions. Generation cost is calculated and the pr...The aim of this paper is to reduce the losses, total generation cost by switching of transmission line and to maintain voltage security under N - 1 contingency conditions. Generation cost is calculated and the priority list is made for switching the line. The problem is solved by ACOPF using Interior Point Method. In order to test the feasibility and effectiveness of the above method, a sample 6-bus system and IEEE 30-bus system have been used. The impact of switching on system parameter includes the generation cost, locational marginal pricing (LMP) and transmission losses, ensuring voltage security of the system.展开更多
A new 3D layout algorithm to lay rectangular tiles on the 3D hull surface model is proposed to improve the algorithm performance in accelerating layout process and enhancing design accuracy. Three times optimizations ...A new 3D layout algorithm to lay rectangular tiles on the 3D hull surface model is proposed to improve the algorithm performance in accelerating layout process and enhancing design accuracy. Three times optimizations are carried out upon the original basic algorithm, namely optimization of calculating range, separation of surface flattening computation from laying computation, and optimization of interior point distribution. By testing, the generated surface layout drawing by the refined system is fairly applicable to guide the actual tiles' coating process.展开更多
A tumor is referred to as“intracranial hard neoplasm”if it grows near the brain or central spinal vessel(neoplasm).In certain cases,it is possible that the responsible cells are neurons situated deep inside the brai...A tumor is referred to as“intracranial hard neoplasm”if it grows near the brain or central spinal vessel(neoplasm).In certain cases,it is possible that the responsible cells are neurons situated deep inside the brain’s structure.This article discusses a strategy for halting the progression of brain tumor.A precise and accurate analytical model of brain tumors is the foundation of this strategy.It is based on an algorithm known as kill chain interior point(KCIP),which is the result of a merger of kill chain and interior point algorithms,as well as a precise and accurate analytical model of brain tumors.The inability to obtain a clear picture of tumor cell activity is the biggest challenge in this endeavor.Based on the motion of swarm robots,which are considered a subset of artificial intelligence,this article proposes a new notion of this kind of behavior,which may be used in various situations.The KCIP algorithm that follows is used in the analytical model to limit the development of certain cell types.According to the findings,it seems that different KCIP speed ratios are beneficial in preventing the development of brain tumors.It is hoped that this study will help researchers better understand the behavior of brain tumors,so as to develop a new drug that is effective in eliminating the tumor cells.展开更多
The paper presents a technique for solving the binary linear programming model in polynomial time. The general binary linear programming problem is transformed into a convex quadratic programming problem. The convex q...The paper presents a technique for solving the binary linear programming model in polynomial time. The general binary linear programming problem is transformed into a convex quadratic programming problem. The convex quadratic programming problem is then solved by interior point algorithms. This settles one of the open problems of whether P = NP or not. The worst case complexity of interior point algorithms for the convex quadratic problem is polynomial. It can also be shown that every liner integer problem can be converted into binary linear problem.展开更多
In this paper we propose an affine scaling interior algorithm via conjugate gradient path for solving nonlinear equality systems subject to bounds on variables. By employing the affine scaling conjugate gradient path ...In this paper we propose an affine scaling interior algorithm via conjugate gradient path for solving nonlinear equality systems subject to bounds on variables. By employing the affine scaling conjugate gradient path search strategy, we obtain an iterative direction by solving the linearize model. By using the line search technique, we will find an acceptable trial step length along this direction which is strictly feasible and makes the objective func- tion nonmonotonically decreasing. The global convergence and fast local convergence rate of the proposed algorithm are established under some reasonable conditions. Furthermore, the numerical results of the proposed algorithm indicate to be effective.展开更多
基金the National Natural Science Foundation of China(No.61601296,61201244)the Science and Technology Innovation Action Plan Project of Shanghai Science and Technology Commission(No.20511103500)the Talent Program of Shanghai University of Engineering Science(No.2018RC43)。
文摘In order to reduce the intrinsic interference of the filter bank multicarrier-quadrature amplitude modulation(FBMC-QAM)system,a novel filter optimization scheme based on discrete prolate spheroidal sequences(DPSS)is proposed.Firstly,a prototype filter function based on DPSS is designed,since the eigenvalue can be used as an indicator of the energy concentration of DPSS,so a threshold is set,and the sequence with the most concentrated energy is selected under the threshold,that is,the sequence with the eigenvalue higher than the threshold,and the prototype filter function is rewritten as a weighted sum function of multiple eigenvectors.Under the energy constraints of the filter,the relationship between the eigenvectors and the intrinsic interference function is established,and the function problem is transformed into an optimization problem for the weighted coefficients.Through the interior point method,the most suitable weight is found to obtain the minimum intrinsic interference result.Theoretical analysis and simulation results show that compared with the prototype filters such as Type1 and CaseC,the DPSS filter applying the proposed optimization algorithm can effectively suppress the intrinsic interference of the system and obtain a better bit error rate(BER)performance.
文摘In this paper, on the basis of the logarithmic barrier function and KKT conditions, we propose a combined homotopy infeasible interior-point method (CHIIP) for convex nonlinear programming problems. For any convex nonlinear programming, without strict convexity for the logarithmic barrier function, we get different solutions of the convex programming in different cases by CHIIP method.
基金supported by the National Natural Science Foundation of China (Grant No.10771133)the Shanghai Leading Academic Discipline Project (Grant Nos.J50101, S30104)
文摘A penalized interior point approach for constrained nonlinear programming is examined in this work. To overcome the difficulty of initialization for the interior point method, a problem equivalent to the primal problem via incorporating an auxiliary variable is constructed. A combined approach of logarithm barrier and quadratic penalty function is proposed to solve the problem. Based on Newton's method, the global convergence of interior point and line search algorithm is proven. Only a finite number of iterations is required to reach an approximate optimal solution. Numerical tests are given to show the effectiveness of the method.
基金Project supported by the National Natural Science Foundation of China (Grant No.10872163)the Natural Science Foundation of Education Department of Shaanxi Province (Grant No.08JK394)
文摘The element-free Galerkin method is proposed to solve free vibration of rectangular plates with finite interior elastic point supports and elastically restrained edges.Based on the extended Hamilton's principle for the elastic dynamics system,the dimensionless equations of motion of rectangular plates with finite interior elastic point supports and the edge elastically restrained are established using the element-free Galerkin method.Through numerical calculation,curves of the natural frequency of thin plates with three edges simply supported and one edge elastically restrained,and three edges clamped and the other edge elastically restrained versus the spring constant,locations of elastic point support and the elastic stiffness of edge elastically restrained are obtained.Effects of elastic point supports and edge elastically restrained on the free vibration characteristics of the thin plates are analyzed.
文摘In this paper, we propose a primal-dual interior point method for solving general constrained nonlinear programming problems. To avoid the situation that the algorithm we use may converge to a saddle point or a local maximum, we utilize a merit function to guide the iterates toward a local minimum. Especially, we add the parameter ε to the Newton system when calculating the decrease directions. The global convergence is achieved by the decrease of a merit function. Furthermore, the numerical results confirm that the algorithm can solve this kind of problems in an efficient way.
基金Supported by the NNSF of China(11026079)Supported by the Youth Backbone Teacher Foundation of Henan Province(173)
文摘In this paper,we are mainly devoted to solving fixed point problems in more general nonconvex sets via an interior point homotopy method.Under suitable conditions,a constructive proof is given to prove the existence of fixed points,which can lead to an implementable globally convergent algorithm.
基金The NNSF (10071031) of China and National 973 Project.
文摘The finite-dimensional variational inequality problem (VIP) has been studied extensively in the literature because of its successful applications in many fields such as economics, transportation, regional science and operations research. Barker and Pang[1] have given an excellent survey of theories, methods and applications of VIPs.
文摘Low-order wavefront error account for a large proportion of wave aberrations.A compensation method for low order aberration of projection lithography objective based on Interior Point Method is presented.Compensation model between wavefront error and degree of movable lens freedom is established.Converting over-determined system to underdetermined system,the compensation is solved by Interior Point Method(IPM).The presented method is compared with direct solve the over-determined system.Then,other algorithm GA,EA and PS is compared with IPM.Simulation and experimental results show that the presented compensation method can obtained compensation with less residuals compared with direct solve the over-determined system.Also,the presented compensation method can reduce computation time and obtain results with less residuals compare with AGA,EA and PS.Moreover,after compensation,RMS of wavefront error of the experimental lithography projection objective decrease from 56.05 nm to 17.88 nm.
基金financial support from Council of Scientific and Industrial Research,India through a research fellowship(File No.09/1217(0025)/2017-EMR-I)to carry out this research workDebdas Ghosh acknowledges the research grant(MTR/2021/000696)from SERB,India to carry out this research work.
文摘This paper proposes an interior-point technique for detecting the nondominated points of multi-objective optimization problems using the direction-based cone method.Cone method decomposes the multi-objective optimization problems into a set of single-objective optimization problems.For this set of problems,parametric perturbed KKT conditions are derived.Subsequently,an interior point technique is developed to solve the parametric perturbed KKT conditions.A differentiable merit function is also proposed whose stationary point satisfies the KKT conditions.Under some mild assumptions,the proposed algorithm is shown to be globally convergent.Numerical results of unconstrained and constrained multi-objective optimization test problems are presented.Also,three performance metrics(modified generational distance,hypervolume,inverted generational distance)are used on some test problems to investigate the efficiency of the proposed algorithm.We also compare the results of the proposed algorithm with the results of some other existing popular methods.
基金Supported by the National Natural Science Foundation of China(10901045,11171088)Supported by the NSF of Hebei Province(A2010000828)Supported by the SF of Hebei University of Science and Technology(QD200955)
文摘An interior point of a finite planar point set is a point of the set that is not on the boundary of the convex hull of the set.For any integer fc > 1,let h(k) be the smallest integer such that every set of points in the plane,no three collinear,with at least h(k) interior points,has a subset of points with exactly fc or fc + 1 interior points of P.We prove that h(5) = 11.
基金Supported by the General Project of Education Department of Hunan Province(09C470)
文摘This article establishes several new geometric inequalities, which refer to the lengthes of the edges of a simplex and interior point, height, lateral area, and the circumradius of another simplex.
基金National Natural Science Foundations of China(Nos.51007052,71201097)Natural Science Foundation of Shanghai,China(No.14ZR1415300)
文摘With the rapid development of the wind generation,uncertainties of random wind and load bring some inevitable impacts on the security of power system. Once the uncertainty causes line power to exceed its limit, line overload will occur. The paper presents the risk control of transmission line overload for windintegrated power systems. Firstly, a risk control model of line overload is proposed considering the uncertainties of loads,generator outputs and wind powers. The generation cost and security level of system associated with overload can be optimally controlled. Then path following interior point method is employed to carry out the optimal control. Finally the simulation is made on the modified IEEE-30 bus system. Results show that the risk of line overload is effectively reduced through the optimization of control variables.
文摘In this paper, an unbounded condition is presented, under which we are able to utilize the interior point homotopy method to solve the Brouwer fixed point problem on unbounded sets. Two numerical examples in R3 are presented to illustrate the results in this paper.
文摘The aim of this paper is to reduce the losses, total generation cost by switching of transmission line and to maintain voltage security under N - 1 contingency conditions. Generation cost is calculated and the priority list is made for switching the line. The problem is solved by ACOPF using Interior Point Method. In order to test the feasibility and effectiveness of the above method, a sample 6-bus system and IEEE 30-bus system have been used. The impact of switching on system parameter includes the generation cost, locational marginal pricing (LMP) and transmission losses, ensuring voltage security of the system.
基金Supported by the Fundamental Research and Application Fund for Ship Industry (04J1.13.3)
文摘A new 3D layout algorithm to lay rectangular tiles on the 3D hull surface model is proposed to improve the algorithm performance in accelerating layout process and enhancing design accuracy. Three times optimizations are carried out upon the original basic algorithm, namely optimization of calculating range, separation of surface flattening computation from laying computation, and optimization of interior point distribution. By testing, the generated surface layout drawing by the refined system is fairly applicable to guide the actual tiles' coating process.
文摘A tumor is referred to as“intracranial hard neoplasm”if it grows near the brain or central spinal vessel(neoplasm).In certain cases,it is possible that the responsible cells are neurons situated deep inside the brain’s structure.This article discusses a strategy for halting the progression of brain tumor.A precise and accurate analytical model of brain tumors is the foundation of this strategy.It is based on an algorithm known as kill chain interior point(KCIP),which is the result of a merger of kill chain and interior point algorithms,as well as a precise and accurate analytical model of brain tumors.The inability to obtain a clear picture of tumor cell activity is the biggest challenge in this endeavor.Based on the motion of swarm robots,which are considered a subset of artificial intelligence,this article proposes a new notion of this kind of behavior,which may be used in various situations.The KCIP algorithm that follows is used in the analytical model to limit the development of certain cell types.According to the findings,it seems that different KCIP speed ratios are beneficial in preventing the development of brain tumors.It is hoped that this study will help researchers better understand the behavior of brain tumors,so as to develop a new drug that is effective in eliminating the tumor cells.
文摘The paper presents a technique for solving the binary linear programming model in polynomial time. The general binary linear programming problem is transformed into a convex quadratic programming problem. The convex quadratic programming problem is then solved by interior point algorithms. This settles one of the open problems of whether P = NP or not. The worst case complexity of interior point algorithms for the convex quadratic problem is polynomial. It can also be shown that every liner integer problem can be converted into binary linear problem.
基金the National Science Foundation of China Grant (10471094)the Ph.D.Foundation Grant (0527003) of Chinese Education Ministry+2 种基金the Shanghai Leading Academic Discipline Project (T0401)the Scientific Computing Key Laboratory of Shanghai Universitiesthe Science Foundation Grant (05DZ11) of Shanghai Education Committee
文摘In this paper we propose an affine scaling interior algorithm via conjugate gradient path for solving nonlinear equality systems subject to bounds on variables. By employing the affine scaling conjugate gradient path search strategy, we obtain an iterative direction by solving the linearize model. By using the line search technique, we will find an acceptable trial step length along this direction which is strictly feasible and makes the objective func- tion nonmonotonically decreasing. The global convergence and fast local convergence rate of the proposed algorithm are established under some reasonable conditions. Furthermore, the numerical results of the proposed algorithm indicate to be effective.