In this paper, we study the approximation problem on the closed convex cone, and prove that there exists a unique solution of the approximation problem, then give the algorithm to compute the unique solution.
Some properties for convex cones are discussed, which are used to obtain an equivalent condition and another important property for nearly cone-subconvexlike set-valued functions. Under the nearly cone-subconvexlikene...Some properties for convex cones are discussed, which are used to obtain an equivalent condition and another important property for nearly cone-subconvexlike set-valued functions. Under the nearly cone-subconvexlikeness, some characterizations of the super efficiency are given in terms of scalarization and Lagrangian multipliers. Related results are generalized.展开更多
Some properties of convex cones are obtained and are used to derive several equivalent conditions as well as another important property for nearly cone-subconvexlike set-valued functions. Under the assumption of nearl...Some properties of convex cones are obtained and are used to derive several equivalent conditions as well as another important property for nearly cone-subconvexlike set-valued functions. Under the assumption of nearly cone-subconvexlikeness,a Lagrangian multiplier theorem on Benson proper efficiency is presented. Related results are generalized.展开更多
Nonlinear convex cone programming(NCCP)models have found many practical applications.In this paper,we introduce a flexible first-order primal-dual algorithm,called the variant auxiliary problem principle(VAPP),for sol...Nonlinear convex cone programming(NCCP)models have found many practical applications.In this paper,we introduce a flexible first-order primal-dual algorithm,called the variant auxiliary problem principle(VAPP),for solving NCCP problems when the objective function and constraints are convex but may be nonsmooth.At each iteration,VAPP generates a nonlinear approximation of the primal augmented Lagrangian model.The approximation incorporates both linearization and a distance-like proximal term,and then the iterations of VAPP are shown to possess a decomposition property for NCCP.Motivated by recent applications in big data analytics,there has been a growing interest in the convergence rate analysis of algorithms with parallel computing capabilities for large scale optimization problems.We establish O(1/t)convergence rate towards primal optimality,feasibility and dual optimality.By adaptively setting parameters at different iterations,we show an O(1/t2)rate for the strongly convex case.Finally,we discuss some issues in the implementation of VAPP.展开更多
In this paper, we consider a countable family of surjective mappings {Tn}n∈N satisfying certain quasi-contractive conditions. We also construct a convergent sequence { Xn } n c∈Nby the quasi-contractive conditions o...In this paper, we consider a countable family of surjective mappings {Tn}n∈N satisfying certain quasi-contractive conditions. We also construct a convergent sequence { Xn } n c∈Nby the quasi-contractive conditions of { Tn } n ∈N and the boundary condition of a given complete and closed subset of a cone metric space X with convex structure, and then prove that the unique limit x＂ of {xn}n∈N is the unique common fixed point of {Tn}n∈N. Finally, we will give more generalized common fixed point theorem for mappings {Ti,j}i,j∈N. The main theorems in this paper generalize and improve many known common fixed point theorems for a finite or countable family of mappings with quasi-contractive conditions.展开更多
A new common fixed point result for a countable family of non-self mappings defined on a closed subset of a cone metric space with the convex property is obtained, and from which, a more general result is given. Our m...A new common fixed point result for a countable family of non-self mappings defined on a closed subset of a cone metric space with the convex property is obtained, and from which, a more general result is given. Our main results improve and generalize many known common fixed point theorems.展开更多
In classical convex optimization theory, the Karush-Kuhn-Tucker (KKT) optimality conditions are necessary and sufficient for optimality if the objective as well as the constraint functions involved is convex. Recently...In classical convex optimization theory, the Karush-Kuhn-Tucker (KKT) optimality conditions are necessary and sufficient for optimality if the objective as well as the constraint functions involved is convex. Recently, Lassere [1] considered a scalar programming problem and showed that if the convexity of the constraint functions is replaced by the convexity of the feasible set, this crucial feature of convex programming can still be preserved. In this paper, we generalize his results by making them applicable to vector optimization problems (VOP) over cones. We consider the minimization of a cone-convex function over a convex feasible set described by cone constraints that are not necessarily cone-convex. We show that if a Slater-type cone constraint qualification holds, then every weak minimizer of (VOP) is a KKT point and conversely every KKT point is a weak minimizer. Further a Mond-Weir type dual is formulated in the modified situation and various duality results are established.展开更多
In this paper, we introduce the concept of a (weak) minimizer of order k for a nonsmooth vector optimization problem over cones. Generalized classes of higher-order cone-nonsmooth (F, ρ)-convex functions are introduc...In this paper, we introduce the concept of a (weak) minimizer of order k for a nonsmooth vector optimization problem over cones. Generalized classes of higher-order cone-nonsmooth (F, ρ)-convex functions are introduced and sufficient optimality results are proved involving these classes. Also, a unified dual is associated with the considered primal problem, and weak and strong duality results are established.展开更多
The author gives a dual characterization of solid cones in locally convex spaces. From this the author obtains some criteria for judging convex cones to be solid in various kinds of locally convex spaces. Using a gene...The author gives a dual characterization of solid cones in locally convex spaces. From this the author obtains some criteria for judging convex cones to be solid in various kinds of locally convex spaces. Using a general expression of the interior of a solid cone, the author obtains a number of necessary and sufficient conditions for convex cones to be solid in the framework of Banach spaces. In particular, the author gives a dual relationship between solid cones and generalized sharp cones. The related known results are improved and extended.展开更多
针对基于能量管理的高速飞行器轨迹优化问题,考虑发动机工作过程对飞行状态严格的约束要求,提出一种基于凸优化的高速飞行器轨迹优化方法。即认为发动机燃油耗尽关机、飞行器动力一定的前提下,求解射程最远的优化轨迹以满足高速长远距...针对基于能量管理的高速飞行器轨迹优化问题,考虑发动机工作过程对飞行状态严格的约束要求,提出一种基于凸优化的高速飞行器轨迹优化方法。即认为发动机燃油耗尽关机、飞行器动力一定的前提下,求解射程最远的优化轨迹以满足高速长远距离飞行任务需求。首先,在飞行器纵向动力学质点模型基础上进行简化处理,得到以飞行器质量为变量的四阶动力学方程,将考虑发动机工作约束的飞行器射程的最优轨迹求解问题,转化为一系列非线性规划问题;接着,将非线性规划问题转化为二阶锥规划(Second Order Cone Program,SOCP)问题,对动力学方程以及不等式约束线性化、离散化处理后,采用原对偶内点法求解,获得最优轨迹;最后,仿真验证了所提优化方法在发动机工作约束范围内,解得了射程最大的最优轨迹。展开更多
A multicriterion clustering model with cone dominated structure is established and the concept of cone-efficient clustering is put forward. The properties of cone-efficient clustering are disscussed, and a method to s...A multicriterion clustering model with cone dominated structure is established and the concept of cone-efficient clustering is put forward. The properties of cone-efficient clustering are disscussed, and a method to solve multicriterion clustering is put forward.The model of Ref.[3] is a special case of that proposed in this paper.展开更多
In this paper, the existence theorem of the cone weak subdifferential of set valued mapping in locally convex topological vector space is proved. Received March 30,1998. 1991 MR Subject Classification: 4...In this paper, the existence theorem of the cone weak subdifferential of set valued mapping in locally convex topological vector space is proved. Received March 30,1998. 1991 MR Subject Classification: 47H17,90C29.展开更多
提出一种在低空场景下基于接收信号强度(Rcecived Signal Strength,RSS)与到达角度(Angle of Arrival,AOA)信息融合的单站无源定位算法。该算法采用单架无人机设备虚拟多站设备接收无线电辐射源信号,融合RSS估计的距离信息与AOA方向角信...提出一种在低空场景下基于接收信号强度(Rcecived Signal Strength,RSS)与到达角度(Angle of Arrival,AOA)信息融合的单站无源定位算法。该算法采用单架无人机设备虚拟多站设备接收无线电辐射源信号,融合RSS估计的距离信息与AOA方向角信息,依据最小二乘准则(LS)构造算法的优化目标函数,采用凸松弛技术将目标函数等价为二阶锥规划(SOCP)问题并通过内点法求解。实验结果表明,该算法的定位精度在2 km范围内可达20 m,其定位性能优于单站无源定位算法,且由于采用单架无人机采集信号,其设备复杂度相较于多站无源定位较低。展开更多
基金Research supported by National Natural Science Foundation of China(10171031).
文摘In this paper, we study the approximation problem on the closed convex cone, and prove that there exists a unique solution of the approximation problem, then give the algorithm to compute the unique solution.
文摘Some properties for convex cones are discussed, which are used to obtain an equivalent condition and another important property for nearly cone-subconvexlike set-valued functions. Under the nearly cone-subconvexlikeness, some characterizations of the super efficiency are given in terms of scalarization and Lagrangian multipliers. Related results are generalized.
文摘Some properties of convex cones are obtained and are used to derive several equivalent conditions as well as another important property for nearly cone-subconvexlike set-valued functions. Under the assumption of nearly cone-subconvexlikeness,a Lagrangian multiplier theorem on Benson proper efficiency is presented. Related results are generalized.
基金This research was supported by the National Natural Science Foundation of China(Nos.71471112 and 71871140).
文摘Nonlinear convex cone programming(NCCP)models have found many practical applications.In this paper,we introduce a flexible first-order primal-dual algorithm,called the variant auxiliary problem principle(VAPP),for solving NCCP problems when the objective function and constraints are convex but may be nonsmooth.At each iteration,VAPP generates a nonlinear approximation of the primal augmented Lagrangian model.The approximation incorporates both linearization and a distance-like proximal term,and then the iterations of VAPP are shown to possess a decomposition property for NCCP.Motivated by recent applications in big data analytics,there has been a growing interest in the convergence rate analysis of algorithms with parallel computing capabilities for large scale optimization problems.We establish O(1/t)convergence rate towards primal optimality,feasibility and dual optimality.By adaptively setting parameters at different iterations,we show an O(1/t2)rate for the strongly convex case.Finally,we discuss some issues in the implementation of VAPP.
基金supported by the National Natural Science Foundation of China (No. 11261062 and No. 11361064)
文摘In this paper, we consider a countable family of surjective mappings {Tn}n∈N satisfying certain quasi-contractive conditions. We also construct a convergent sequence { Xn } n c∈Nby the quasi-contractive conditions of { Tn } n ∈N and the boundary condition of a given complete and closed subset of a cone metric space X with convex structure, and then prove that the unique limit x＂ of {xn}n∈N is the unique common fixed point of {Tn}n∈N. Finally, we will give more generalized common fixed point theorem for mappings {Ti,j}i,j∈N. The main theorems in this paper generalize and improve many known common fixed point theorems for a finite or countable family of mappings with quasi-contractive conditions.
基金Foundation item： Supported by the National Natural Science Foundation of China（11361064）
文摘A new common fixed point result for a countable family of non-self mappings defined on a closed subset of a cone metric space with the convex property is obtained, and from which, a more general result is given. Our main results improve and generalize many known common fixed point theorems.
文摘In classical convex optimization theory, the Karush-Kuhn-Tucker (KKT) optimality conditions are necessary and sufficient for optimality if the objective as well as the constraint functions involved is convex. Recently, Lassere [1] considered a scalar programming problem and showed that if the convexity of the constraint functions is replaced by the convexity of the feasible set, this crucial feature of convex programming can still be preserved. In this paper, we generalize his results by making them applicable to vector optimization problems (VOP) over cones. We consider the minimization of a cone-convex function over a convex feasible set described by cone constraints that are not necessarily cone-convex. We show that if a Slater-type cone constraint qualification holds, then every weak minimizer of (VOP) is a KKT point and conversely every KKT point is a weak minimizer. Further a Mond-Weir type dual is formulated in the modified situation and various duality results are established.
文摘In this paper, we introduce the concept of a (weak) minimizer of order k for a nonsmooth vector optimization problem over cones. Generalized classes of higher-order cone-nonsmooth (F, ρ)-convex functions are introduced and sufficient optimality results are proved involving these classes. Also, a unified dual is associated with the considered primal problem, and weak and strong duality results are established.
基金the National Natural Science Foundation of China(10571035)
文摘The author gives a dual characterization of solid cones in locally convex spaces. From this the author obtains some criteria for judging convex cones to be solid in various kinds of locally convex spaces. Using a general expression of the interior of a solid cone, the author obtains a number of necessary and sufficient conditions for convex cones to be solid in the framework of Banach spaces. In particular, the author gives a dual relationship between solid cones and generalized sharp cones. The related known results are improved and extended.
文摘针对基于能量管理的高速飞行器轨迹优化问题,考虑发动机工作过程对飞行状态严格的约束要求,提出一种基于凸优化的高速飞行器轨迹优化方法。即认为发动机燃油耗尽关机、飞行器动力一定的前提下,求解射程最远的优化轨迹以满足高速长远距离飞行任务需求。首先,在飞行器纵向动力学质点模型基础上进行简化处理,得到以飞行器质量为变量的四阶动力学方程,将考虑发动机工作约束的飞行器射程的最优轨迹求解问题,转化为一系列非线性规划问题;接着,将非线性规划问题转化为二阶锥规划(Second Order Cone Program,SOCP)问题,对动力学方程以及不等式约束线性化、离散化处理后,采用原对偶内点法求解,获得最优轨迹;最后,仿真验证了所提优化方法在发动机工作约束范围内,解得了射程最大的最优轨迹。
文摘A multicriterion clustering model with cone dominated structure is established and the concept of cone-efficient clustering is put forward. The properties of cone-efficient clustering are disscussed, and a method to solve multicriterion clustering is put forward.The model of Ref.[3] is a special case of that proposed in this paper.
文摘In this paper, the existence theorem of the cone weak subdifferential of set valued mapping in locally convex topological vector space is proved. Received March 30,1998. 1991 MR Subject Classification: 47H17,90C29.
文摘提出一种在低空场景下基于接收信号强度(Rcecived Signal Strength,RSS)与到达角度(Angle of Arrival,AOA)信息融合的单站无源定位算法。该算法采用单架无人机设备虚拟多站设备接收无线电辐射源信号,融合RSS估计的距离信息与AOA方向角信息,依据最小二乘准则(LS)构造算法的优化目标函数,采用凸松弛技术将目标函数等价为二阶锥规划(SOCP)问题并通过内点法求解。实验结果表明,该算法的定位精度在2 km范围内可达20 m,其定位性能优于单站无源定位算法,且由于采用单架无人机采集信号,其设备复杂度相较于多站无源定位较低。
