Banach空间中向量优化问题解集的刻画

在有限维空间中,当目标函数凸下半连续时,向量优化问题一定有解,并且解集是紧的。但在无穷维空间中,这不一定成立。不过可以通过在对偶空间中构造一个集合,减弱对目标函数的假设之后,把之前关于有限维空间中向量优化问题的解集的研究,推广到实自反Banach空间中。     

A subdifferential characterization of Motzkin decomposable functions

Abstract

The paper provides a new subdifferential characterization for Motzkin decomposable (convex) functions. This characterization leads to diverse stability properties for such a decomposability for operations like addition and composition.     

The limiting Lagrangian as a consequence of Helly's theorem

The perturbational Lagrangian equation established by Jeroslow in convex semi-infinite programming is derived from Helly's theorem and some prior results on one-dimensional perturbations of convex programs.This research was partially supported by NRC, Grant No. A-4493.     

关于凸包及回收锥性质的研究

主要是应用凸分析中的凸集和回收锥的相关结论,对有限个凸函数集进行研究,由此得到了关于凸函数集{f1,…,fm}的凸包及回收锥的两个重要性质.     

补贴退坡-双积分政策下两级供应链生产决策优化分析

在退坡与双积分政策下, 分析由一个车企和一个分销商组成的两级供应链中的生产决策问题。基于Stackelberg博弈, 阐释退坡和双积分对车企与分销商最优决策的影响。对比分析集中决策和分散决策对供应链绩效的影响, 帮助汽车供应链有效适应“双积分”政策。研究表明:在双积分政策未实施时, 随着补贴的不断降低, 新能源汽车的需求量、车企的利润会随之降低; 双积分政策实施之后, 车企不断提高研发努力水平可使新能源汽车的需求量提高, 车企与分销商的利润可获得帕累托改进。数值分析表明, 双积分政策可以有效促进新能源汽车的发展。     

Structure of closed finitely starshaped sets

A set is finitely starshaped if any finite subset of is totally visible from some point of . It is well known that in a finite-dimensional linear space, a closed finitely starshaped set which is not starshaped must be unbounded. It is proved here that such a set must admit at least one direction of recession. This fact clarifies the structure of such sets and allows the study of properties of their visibility elements, well known in the case of starshaped sets. A characterization of planar finitely starshaped sets by means of its convex components is obtained. Some plausible conjectures are disproved by means of counterexamples.     

Convergence Properties of a Conditional ε-Subgradient Method Applied to Linear Programs

We propose a new conditional ε-subgradient method intended for solving general convex programs, Convergence properties of the method are investigated. It is proved that for a linear program with a compact set of solutions, the method generates a sequence of feasible approximations whose objective function values converge to the optimal value at a rate that is at least linear.     

Weighting factor results in vector optimization

This paper deals with the study, in a convex vector optimization problem, of the set of efficient solutions and the set of properly efficient solutions, the latter being obtained by a weighting factor technique. Relationships between these two sets are discussed; they are shown to be nonempty when the objective functions have no common direction of recession and to be closed and equal when, moreover, the objective functions are locally polyhedral. An example is provided where the set of efficient solutions is not included in the closure of the nonempty set of properly efficient solutions.The author wishes to thank the unknown referee for the helpful comments that improved the quality of this paper.     

On Generalizations of the Frank-Wolfe Theorem to Convex and Quasi-Convex Programmes

In this paper we are concerned with the problem of boundedness and the existence of optimal solutions to the constrained optimization problem. We present necessary and sufficient conditions for boundedness of either a faithfully convex or a quasi-convex polynomial function over the feasible set defined by a system of faithfully convex inequality constraints and/or quasi-convex polynomial inequalities, where the faithfully convex functions satisfy some mild assumption. The conditions are provided in the form of an algorithm, terminating after a finite number of iterations, the implementation of which requires the identification of implicit equality constraints in a homogeneous linear system. We prove that the optimal solution set of the considered problem is nonempty, this way extending the attainability result well known as the so-called Frank-Wolfe theorem. Finally we show that our extension of the Frank-Wolfe theorem immediately implies continuity of the solution set defined by the considered system of (quasi)convex inequalities.     

Primal and Dual Stability Results for Variational Inequalities

The purpose of this paper is to study the continuous dependence of solutions of variational inequalities with respect to perturbations of the data that are maximal monotone operators and closed convex functions. The constraint sets are defined by a finite number of linear equalities and non linear convex inequalities. Primal and dual stability results are given, extending the classical ones for optimization problems.