Active set method and gradient projection method are curre nt ly the main approaches for linearly constrained convex programming. Interior-po int method is one of the most effective choices for linear programming. In ...Active set method and gradient projection method are curre nt ly the main approaches for linearly constrained convex programming. Interior-po int method is one of the most effective choices for linear programming. In the p aper a predictor-corrector interior-point algorithm for linearly constrained c onvex programming under the predictor-corrector motivation was proposed. In eac h iteration, the algorithm first performs a predictor-step to reduce the dualit y gap and then a corrector-step to keep the points close to the central traject ory. Computations in the algorithm only require that the initial iterate be nonn egative while feasibility or strict feasibility is not required. It is proved th at the algorithm is equivalent to a level-1 perturbed composite Newton method. Numerical experiments on twenty-six standard test problems are made. The result s show that the proposed algorithm is stable and robust.展开更多
A new class of generalized constrained multiobjective games is introduced and studied in locally FC-uniform spaces without convexity structure where the number of players may be finite or infinite and all payoff funct...A new class of generalized constrained multiobjective games is introduced and studied in locally FC-uniform spaces without convexity structure where the number of players may be finite or infinite and all payoff functions get their values in an infinite-dimensional space. By using a Himmelberg type fixed point theorem in locally FC-uniform spaces due to author, some existence theorems of weak Paxeto equilibria for the generalized constrained multiobjective games are established in locally FC-uniform spaces. These theorems improve, unify and generalize the corresponding results in recent literatures.展开更多
Cancer immunotherapy aims at enhancing immune system to defend against the tumor. However, it is associated with injecting small doses of tumor-bearing molecules or even using drugs. The problem is that how to schedul...Cancer immunotherapy aims at enhancing immune system to defend against the tumor. However, it is associated with injecting small doses of tumor-bearing molecules or even using drugs. The problem is that how to schedule these injections effectively and/or how to apply drugs in a way to decrease toxic side effects of drugs such that the tumor growth to be stopped or at least to be limited. Here, the theory of optimal control has been applied to find the optimal schedule of injections of an immunotherapeutic agent against cancer. The numerical method employed works for any dynamic linear system and has almost precise solution. In this work, it was tested for a well known model of the tumor immune system interaction.展开更多
We consider the so-called Thomson problem which refers to finding the equilibrium distribution of a finite number of mutually repelling point charges on the surface of a sphere, but for the case where the sphere is re...We consider the so-called Thomson problem which refers to finding the equilibrium distribution of a finite number of mutually repelling point charges on the surface of a sphere, but for the case where the sphere is replaced by a spheroid or ellipsoid. To get started, we first consider the problem in two dimensions, with point charges on circles (for which the equilibrium distribution is intuitively obvious) and ellipses. We then generalize the approach to the three-dimensional case of an ellipsoid. The method we use is to begin with a random distribution of charges on the surface and allow each point charge to move tangentially to the surface due to the sum of all Coulomb forces it feels from the other charges. Deriving the proper equations of motion requires using a projection operator to project the total force on each point charge onto the tangent plane of the surface. The position vectors then evolve and find their final equilibrium distribution naturally. For the case of ellipses and ellipsoids or spheroids, we find that multiple distinct equilibria are possible for certain numbers of charges, depending on the starting conditions. We characterize these based on their total potential energies. Some of the equilibria found turn out to represent local minima in the potential energy landscape, while others represent the global minimum. We devise a method based on comparing the moment-of-inertia tensors of the final configurations to distinguish them from one another.展开更多
In this article, we introduce and study some new classes of multi-leader-follower generalized constrained multiobjective games in locally FC-uniform spaces where the number of leaders and followers may be finite or in...In this article, we introduce and study some new classes of multi-leader-follower generalized constrained multiobjective games in locally FC-uniform spaces where the number of leaders and followers may be finite or infinite and the objective functions of the followers obtain their values in infinite-dimensional spaces. Each leader has a constrained correspondence. By using a collective fixed point theorem in locally FC-uniform spaces due to author, some existence theorems of equilibrium points for the multi-leader-follower generalized constrained multiobjective games are established under nonconvex settings. These results generalize some corresponding results in recent literature.展开更多
We consider a linear-quadratical optimal control problem of a system governed by parabolic equation with distributed in right-hand side control and control and state constraints. We construct a mesh approximation of t...We consider a linear-quadratical optimal control problem of a system governed by parabolic equation with distributed in right-hand side control and control and state constraints. We construct a mesh approximation of this problem using different two-level approximations of the state equation, ADI and fractional steps approximations in time among others. Iterative solution methods are investigated for all constructed approximations of the optimal control problem. Their implementation can be carried out in parallel manner.展开更多
Iterative methods for solving discrete optimal control problems are constructed and investigated. These discrete problems arise when approximating by finite difference method or by finite element method the optimal co...Iterative methods for solving discrete optimal control problems are constructed and investigated. These discrete problems arise when approximating by finite difference method or by finite element method the optimal control problems which contain a linear elliptic boundary value problem as a state equation, control in the righthand side of the equation or in the boundary conditions, and point-wise constraints for both state and control functions. The convergence of the constructed iterative methods is proved, the implementation problems are discussed, and the numerical comparison of the methods is executed.展开更多
A new class of constrained multiobjective games with infinite players in noncompact locally convex H-spaces without linear structure are introduced and studied.By applying a Fan-Glicksberg type fixed point theorem for...A new class of constrained multiobjective games with infinite players in noncompact locally convex H-spaces without linear structure are introduced and studied.By applying a Fan-Glicksberg type fixed point theorem for upper semicontinuous set-valued mappings with closed acyclic values and a maximum theorem,several existence theorems of weighted Nath-equilibria and Pareto equilibria for the constrained multiobjective games are proved in noncompact locally convex H-spaces.These theorems improve,unify and generalize the corresponding results of the multiobjective games in recent literatures.展开更多
In this paper, a new augmented Lagrangian penalty function for constrained optimization problems is studied. The dual properties of the augmented Lagrangian objective penalty function for constrained optimization prob...In this paper, a new augmented Lagrangian penalty function for constrained optimization problems is studied. The dual properties of the augmented Lagrangian objective penalty function for constrained optimization problems are proved. Under some conditions, the saddle point of the augmented Lagrangian objective penalty function satisfies the first-order Karush-Kuhn-Tucker (KKT) condition. Especially, when the KKT condition holds for convex programming its saddle point exists. Based on the augmented Lagrangian objective penalty function, an algorithm is developed for finding a global solution to an inequality constrained optimization problem and its global convergence is also proved under some conditions.展开更多
点云配准广泛应用于机器人检测和场景重建中不同测量位姿数据的融合。然而,针对高铁车体等大尺度场景中常见的平面特征,传统基于点对点距离和点到平面距离的配准方法在初始姿态不佳时易陷入局部极小值。为解决这些问题,提出了一种基于...点云配准广泛应用于机器人检测和场景重建中不同测量位姿数据的融合。然而,针对高铁车体等大尺度场景中常见的平面特征,传统基于点对点距离和点到平面距离的配准方法在初始姿态不佳时易陷入局部极小值。为解决这些问题,提出了一种基于共面约束的鲁棒多维点云配准方法。首先,对二维平面特征中的点云进行投影,并定义二维点对点(point-to-point in twodimension,PTP-2D)距离以约束不同平面特征之间的距离。该约束能够有效规避局部极小值,但会引发平移向量解的非唯一性。因此,引入三维点到点(point-to-point in three-dimension,PTP-3D)约束以限定平移向量解集,并进一步定义多维点到点距离(point-to-point in multidimension,PTP-MD)平衡收敛速度与配准精度。为验证PTP-MD方法的有效性,将其与四种经典配准方法在高速列车车身点云上进行了对比。试验结果表明,相比于传统的点云匹配方法,该方法能够显著摆脱局部极小值。展开更多
随着新能源发电比例越来越高,其受电网三相不平衡的影响越来越明显,尤其负序超标是导致电力系统安全性降低的重要原因。统一潮流控制器(unified power flow controller,UPFC)具有调节各序电流输出的能力,可用于提升系统的平衡性。为此,...随着新能源发电比例越来越高,其受电网三相不平衡的影响越来越明显,尤其负序超标是导致电力系统安全性降低的重要原因。统一潮流控制器(unified power flow controller,UPFC)具有调节各序电流输出的能力,可用于提升系统的平衡性。为此,首先建立基于解耦-补偿原理的UPFC正序最优补偿潮流算法;其次构建UPFC的负序补偿电流控制模型,将电压不平衡补偿的优化求解问题归结为凸二次约束二次规划(quadratically constrained quadratic programming,QCQP)问题,并采用原-对偶内点法求取UPFC的负序电流最优输出值;最后提出计及正序网损与负序电压指标的负序电压补偿最优潮流(optimal power flow,OPF)计算方法以及区域负序电压总体补偿策略。通过算例分析验证所提出方法的可行性与有效性。展开更多
针对带基数约束凸优化问题,提出了一个基于非线性DC(Difference of two convex functions)逼近函数的序列凸优化算法,并证明了该算法收敛到DC逼近问题的KKT(Karush-Kuhn-Tucker)点。数值实验结果表明:基于非线性DC逼近函数的序列凸优化...针对带基数约束凸优化问题,提出了一个基于非线性DC(Difference of two convex functions)逼近函数的序列凸优化算法,并证明了该算法收敛到DC逼近问题的KKT(Karush-Kuhn-Tucker)点。数值实验结果表明:基于非线性DC逼近函数的序列凸优化算法能有效找到带基数约束凸优化问题的稀疏解,且得到解的质量优于已有算法。展开更多
文摘Active set method and gradient projection method are curre nt ly the main approaches for linearly constrained convex programming. Interior-po int method is one of the most effective choices for linear programming. In the p aper a predictor-corrector interior-point algorithm for linearly constrained c onvex programming under the predictor-corrector motivation was proposed. In eac h iteration, the algorithm first performs a predictor-step to reduce the dualit y gap and then a corrector-step to keep the points close to the central traject ory. Computations in the algorithm only require that the initial iterate be nonn egative while feasibility or strict feasibility is not required. It is proved th at the algorithm is equivalent to a level-1 perturbed composite Newton method. Numerical experiments on twenty-six standard test problems are made. The result s show that the proposed algorithm is stable and robust.
基金the Natural Science Foundation of Education Department of Sichuan Province of China(No.07ZA092)the Foundation of Taiwan Science Council
文摘A new class of generalized constrained multiobjective games is introduced and studied in locally FC-uniform spaces without convexity structure where the number of players may be finite or infinite and all payoff functions get their values in an infinite-dimensional space. By using a Himmelberg type fixed point theorem in locally FC-uniform spaces due to author, some existence theorems of weak Paxeto equilibria for the generalized constrained multiobjective games are established in locally FC-uniform spaces. These theorems improve, unify and generalize the corresponding results in recent literatures.
文摘Cancer immunotherapy aims at enhancing immune system to defend against the tumor. However, it is associated with injecting small doses of tumor-bearing molecules or even using drugs. The problem is that how to schedule these injections effectively and/or how to apply drugs in a way to decrease toxic side effects of drugs such that the tumor growth to be stopped or at least to be limited. Here, the theory of optimal control has been applied to find the optimal schedule of injections of an immunotherapeutic agent against cancer. The numerical method employed works for any dynamic linear system and has almost precise solution. In this work, it was tested for a well known model of the tumor immune system interaction.
文摘We consider the so-called Thomson problem which refers to finding the equilibrium distribution of a finite number of mutually repelling point charges on the surface of a sphere, but for the case where the sphere is replaced by a spheroid or ellipsoid. To get started, we first consider the problem in two dimensions, with point charges on circles (for which the equilibrium distribution is intuitively obvious) and ellipses. We then generalize the approach to the three-dimensional case of an ellipsoid. The method we use is to begin with a random distribution of charges on the surface and allow each point charge to move tangentially to the surface due to the sum of all Coulomb forces it feels from the other charges. Deriving the proper equations of motion requires using a projection operator to project the total force on each point charge onto the tangent plane of the surface. The position vectors then evolve and find their final equilibrium distribution naturally. For the case of ellipses and ellipsoids or spheroids, we find that multiple distinct equilibria are possible for certain numbers of charges, depending on the starting conditions. We characterize these based on their total potential energies. Some of the equilibria found turn out to represent local minima in the potential energy landscape, while others represent the global minimum. We devise a method based on comparing the moment-of-inertia tensors of the final configurations to distinguish them from one another.
基金supported by the Scientific Research Fun of Sichuan Normal University(11ZDL01)the Sichuan Province Leading Academic Discipline Project(SZD0406)
文摘In this article, we introduce and study some new classes of multi-leader-follower generalized constrained multiobjective games in locally FC-uniform spaces where the number of leaders and followers may be finite or infinite and the objective functions of the followers obtain their values in infinite-dimensional spaces. Each leader has a constrained correspondence. By using a collective fixed point theorem in locally FC-uniform spaces due to author, some existence theorems of equilibrium points for the multi-leader-follower generalized constrained multiobjective games are established under nonconvex settings. These results generalize some corresponding results in recent literature.
文摘We consider a linear-quadratical optimal control problem of a system governed by parabolic equation with distributed in right-hand side control and control and state constraints. We construct a mesh approximation of this problem using different two-level approximations of the state equation, ADI and fractional steps approximations in time among others. Iterative solution methods are investigated for all constructed approximations of the optimal control problem. Their implementation can be carried out in parallel manner.
文摘Iterative methods for solving discrete optimal control problems are constructed and investigated. These discrete problems arise when approximating by finite difference method or by finite element method the optimal control problems which contain a linear elliptic boundary value problem as a state equation, control in the righthand side of the equation or in the boundary conditions, and point-wise constraints for both state and control functions. The convergence of the constructed iterative methods is proved, the implementation problems are discussed, and the numerical comparison of the methods is executed.
文摘A new class of constrained multiobjective games with infinite players in noncompact locally convex H-spaces without linear structure are introduced and studied.By applying a Fan-Glicksberg type fixed point theorem for upper semicontinuous set-valued mappings with closed acyclic values and a maximum theorem,several existence theorems of weighted Nath-equilibria and Pareto equilibria for the constrained multiobjective games are proved in noncompact locally convex H-spaces.These theorems improve,unify and generalize the corresponding results of the multiobjective games in recent literatures.
文摘In this paper, a new augmented Lagrangian penalty function for constrained optimization problems is studied. The dual properties of the augmented Lagrangian objective penalty function for constrained optimization problems are proved. Under some conditions, the saddle point of the augmented Lagrangian objective penalty function satisfies the first-order Karush-Kuhn-Tucker (KKT) condition. Especially, when the KKT condition holds for convex programming its saddle point exists. Based on the augmented Lagrangian objective penalty function, an algorithm is developed for finding a global solution to an inequality constrained optimization problem and its global convergence is also proved under some conditions.
文摘点云配准广泛应用于机器人检测和场景重建中不同测量位姿数据的融合。然而,针对高铁车体等大尺度场景中常见的平面特征,传统基于点对点距离和点到平面距离的配准方法在初始姿态不佳时易陷入局部极小值。为解决这些问题,提出了一种基于共面约束的鲁棒多维点云配准方法。首先,对二维平面特征中的点云进行投影,并定义二维点对点(point-to-point in twodimension,PTP-2D)距离以约束不同平面特征之间的距离。该约束能够有效规避局部极小值,但会引发平移向量解的非唯一性。因此,引入三维点到点(point-to-point in three-dimension,PTP-3D)约束以限定平移向量解集,并进一步定义多维点到点距离(point-to-point in multidimension,PTP-MD)平衡收敛速度与配准精度。为验证PTP-MD方法的有效性,将其与四种经典配准方法在高速列车车身点云上进行了对比。试验结果表明,相比于传统的点云匹配方法,该方法能够显著摆脱局部极小值。
文摘随着新能源发电比例越来越高,其受电网三相不平衡的影响越来越明显,尤其负序超标是导致电力系统安全性降低的重要原因。统一潮流控制器(unified power flow controller,UPFC)具有调节各序电流输出的能力,可用于提升系统的平衡性。为此,首先建立基于解耦-补偿原理的UPFC正序最优补偿潮流算法;其次构建UPFC的负序补偿电流控制模型,将电压不平衡补偿的优化求解问题归结为凸二次约束二次规划(quadratically constrained quadratic programming,QCQP)问题,并采用原-对偶内点法求取UPFC的负序电流最优输出值;最后提出计及正序网损与负序电压指标的负序电压补偿最优潮流(optimal power flow,OPF)计算方法以及区域负序电压总体补偿策略。通过算例分析验证所提出方法的可行性与有效性。
文摘针对带基数约束凸优化问题,提出了一个基于非线性DC(Difference of two convex functions)逼近函数的序列凸优化算法,并证明了该算法收敛到DC逼近问题的KKT(Karush-Kuhn-Tucker)点。数值实验结果表明:基于非线性DC逼近函数的序列凸优化算法能有效找到带基数约束凸优化问题的稀疏解,且得到解的质量优于已有算法。
