一类概率约束规划逼近最优解集的上半收敛性

对一类概率约束规划逼近最优解集的上半收敛性进行了研究.利用概率测度弱收敛的特征,给出了概率约束规划可行集的收敛性条件,得到了概率约束规划逼近最优解集的上半收敛性.     

概率约束规划逼近最优解集的上半收敛性

本文讨论了概率约束规划目标函数的连续收敛性,并利用概率测度弱收敛的特征给出了概率约束规划可行集的收敛性条件,得到了概率约束规划逼近最优解集的上半收敛性.     

极大极小随机规划逼近问题最优解集和最优值的稳定性

研究了特殊的二层极大极小随机规划逼近收敛问题. 首先将下层初始随机规划最优解集拓展到非单点集情形, 且可行集正则的条件下, 讨论了下层随机规划逼近问题最优解集关于上层决策变量参数的上半收敛性和最优值函数的连续性. 然后把下层随机规划的epsilon-最优解向量函数反馈到上层随机规划的目标函数中, 得到了上层随机规划逼近问题的最优解集关于最小信息概率度量收敛的上半收敛性和最优值的连续性.     

一类极大极小随机规划逼近问题最优解集的上半收敛性

本文首先将极大极小随机规划等价的转化为一个二层随机规划,在下层初始随机规划最优解集为多点集的情形下,给出下层随机规划逼近问题最优解集集值映射关于上层决策变量参数的上半收敛性和最优值函数的连续性.然后将上层随机规划等价转化为以上层和下层决策变量作为整体决策变量,以下层规划最优解集的图作为约束条件的单层规划,并在下层初始随机规划最优解集的图为正则的条件下,得到上层随机规划逼近问题最优解集关于最小信息概率度量收敛的上半收敛性.     

二层随机规划逼近问题最优解集的上半收敛性

在下层初始随机规划问题可行解集上引入了正则的概念,并在下层初始随机规划最优解唯一的条件下,利用上图收敛理论,给出了下层随机规划逼近问题的任意一个最优解向量函数都连续收敛到下层初始随机规划问题的唯一最优解向量函数.然后将下层随机规划的最优解向量函数反馈到上层随机规划的目标函数和约束条件中,得到了上层随机规划逼近问题的最优解集关于最小信息概率度量收敛的上半收敛性.     

非线性参数规划问题ε-最优解集集值映射的连续性

对非线性参数规划问题ε-最优解集集值映射的连续性条件进行了研究.首先在可行集集值映射局部有界且正则的条件下,讨论了非线性参数规划问题最优值函数的连续性,然后针对ε-最优解集集值映射的结构特征并利用此结果和集值分析理论,给出了非线性参数规划问题ε-最优解集集值映射连续的一个充分条件.     

非线性参数规划问题$\varepsilon$-最优解集集值映射的连续性

对非线性参数规划问题$\varepsilon$-最优解集集值映射的连续性条件进行了研究.首先在可行集集值映射局部有界且正则的条件下,讨论了非线性参数规划问题最优值函数的连续性,然后针对$\varepsilon$-最优解集集值映射的结构特征并利用此结果和集值分析理论,给出了非线性参数规划问题$\varepsilon$-最优解集集值映射连续的一个充分条件.     

概率约束随机规划的一种近似方法及其它的有效解模式

根据最小风险的投资最优问题，我们给出了一个统一的概率约束随机规划模型。随后我们提出了求解这类概率约束随机规划的一种近似算法，并在一定的条件下证明了算法的收敛性。此外，提出了这种具有概率约束多目标随机规划问题的一种有效解模型。     

不等式约束随机非线性规划的扰动Karush-Kuhn-Tucker系统的解路径

论文聚焦概率测度发生扰动时的随机非线性规划的稳定性分析的研究.目标函数的Lipschitz连续性和可行集值映射的度量正则性条件可保证最优解集合的外半连续性和最优值的Lipschitz连续性.更重要地,本文证明了,如果原问题的极小点处线性无关约束规范和强二阶充分性条件成立,那么存在一Lipschitz连续的解路径满足扰动问题的Karush-Kuhn-Tucker条件.     

概率约束规划的稳定性分析

本文对概率约束规划问题的稳定性进行了探讨,得出了当随机向量序列{ξ^(k)(ω）}分布收敛于ξ（ω）时,相应于ξ^(k)(ω)的概率约束规划问题的最优值收敛于原问题的最优值,这个结果为设计逼近算法和改进逼近解提供了一个理论基础。     

On the stability of general convex programs under slater’s condition and primal solution boundedness

This paper was motivated by an article by Best and Chakravarti, who presented some stability results for convex quadratic programs under linear perturbation of the data. We show that the regularity conditions assumed are much too restrictive and demonstrate that stronger stability results follow under weaker assumptions (primal solution boundedness and the Slater condition) and from known results, not only for convex quadratic problems but for general convex programs with general perturbations. In so doing, we give a simple and reasonably complete characterization of the stability of an important class of well-behaved convex programs, collecting results that heretofore have apparently not been presented in a unified manner. The results, virtually all from Hogan and Robinson, involve mainly stability of the feasible region and solution existence under small perturbations, and continuity and differentiability of the optimal value function. We note that Auslender and Coutat have recently provided similar extensions for saddle points of generalized linear-quadratic programs introduced by Rockafellar and Wets, utilizing the same assumptions that we use in this paper     

A SUCCESSIVE APPROXIMATION METHOD FOR SOLVING PROBABILISTIC CONSTRAINED PROGRAMS

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Differential stability of solutions to convex,control constrained optimal control problems

A family of convex, control constrained optimal control problems that depend on a real parameter is considered. It is shown that under some regularity conditions on data the solutions of these problems, as well as the associated Lagrange multipliers are directionally differentiable with respect to parameter. The respective right-derivatives are given as the solution and the associated Lagrange multipliers for some quadratic optimal control problem. If a condition of strict complementarity type hold, then directional derivatives become continuous ones.     

Calculus of sequential normal compactness in variational analysis

In this paper we study some properties of sets, set-valued mappings, and extended-real-valued functions unified under the name of “sequential normal compactness.” These properties automatically hold in finite-dimensional spaces, while they play a major role in infinite-dimensional variational analysis. In particular, they are essential for calculus rules involving generalized differential constructions, for stability and metric regularity results and their broad applications, for necessary optimality conditions in constrained optimization and optimal control, etc. This paper contains principal results ensuring the preservation of sequential normal compactness properties under various operations over sets, set-valued mappings, and functions.     

Hölder Continuity of Adjoint States and Optimal Controls for State Constrained Problems

We investigate Hölder regularity of adjoint states and optimal controls for a Bolza problem under state constraints. We start by considering any optimal solution satisfying the constrained maximum principle in its normal form and we show that whenever the associated Hamiltonian function is smooth enough and has some monotonicity properties in the directions normal to the constraints, then both the adjoint state and optimal trajectory enjoy Hölder type regularity. More precisely, we prove that if the state constraints are smooth, then the adjoint state and the derivative of the optimal trajectory are Hölder continuous, while they have the two sided lower Hölder continuity property for less regular constraints. Finally, we provide sufficient conditions for Hölder type regularity of optimal controls.     

Stability analysis for stochastic programs

For stochastic programs with recourse and with (several joint) probabilistic constraints, respectively, we derive quantitative continuity properties of the relevant expectation functionals and constraint set mappings. This leads to qualitative and quantitative stability results for optimal values and optimal solutions with respect to perturbations of the underlying probability distributions. Earlier stability results for stochastic programs with recourse and for those with probabilistic constraints are refined and extended, respectively. Emphasis is placed on equipping sets of probability measures with metrics that one can handle in specific situations. To illustrate the general stability results we present possible consequences when estimating the original probability measure via empirical ones.