A graphical characterization of the efficient set for?convex multiobjective problems

In this paper, a graphical characterization, in the decision space, of the properly efficient solutions of a convex multiobjective problem is derived. This characterization takes into account the relative position of the gradients of the objective functions and the active constraints at the given feasible solution. The unconstrained case with two objective functions and with any number of functions and the general constrained case are studied separately. In some cases, these results can provide a visualization of the efficient set, for problems with two or three variables. Besides, a proper efficiency test for general convex multiobjective problems is derived, which consists of solving a single linear optimization problem.     

Contractibility of the Solution Sets in Strictly Quasiconcave Vector Maximization on Noncompact Domains

We study the contractibility of the efficient solution set of strictly quasiconcave vector maximization problems on (possibly) noncompact feasible domains. It is proved that the efficient solution set is contractible if at least one of the objective functions is strongly quasiconcave and any intersection of level sets of the objective functions is a compact (possibly empty) set. This theorem generalizes the main result of Benoist (Ref.1), which was established for problems on compact feasible domains.The authors thank Dr. T. D. Phuong, Dr. T. X. D. Ha, and the referees for helpful comments and suggestions.     

带关联的双层多目标决策研究

本文研究是线性的双层多目标决策.根据线性规划的对偶理论证明了双层多目标决策的可行集的连通性;利用s*-最优均衡解的概念,求得双层多目标规划的偏好满意解;最后,我们得到了满意解的有效性,并在极点得到.     

Comparison between different duals in multiobjective fractional programming

The present paper is a continuation of [2] where we deal with the duality for a multiobjective fractional optimization problem. The basic idea in [2] consists in attaching an intermediate multiobjective convex optimization problem to the primal fractional problem, using an approach due to Dinkelbach ([6]), for which we construct then a dual problem expressed in terms of the conjugates of the functions involved. The weak, strong and converse duality statements for the intermediate problems allow us to give dual characterizations for the efficient solutions of the initial fractional problem. The aim of this paper is to compare the intermediate dual problem with other similar dual problems known from the literature. We completely establish the inclusion relations between the image sets of the duals as well as between the sets of maximal elements of the image sets.      

参数优化的最优性及在控制问题中的一个应用

在Banach空间中,给出了含参数的单值映射的不变类凸,拟不变类凸和伪不变类凸的概念.在这类较弱凸性条件下,提出了参数优化问题弱有效解的几个最优性充分条件.作为应用,研究了一类状态约束最优控制问题的弱最优控制.     

Connectedness of efficient solution sets for set-valued maps in normed spaces

In vector optimization, the topological properties of the set of efficient solutions are of interest. Several authors have studied this topic for point-valued functions. In this paper, we study the connectedness of the efficient solution sets in convex vector optimization for set-valued maps in normed spaces.The author would like to thank Professor W. T. Fu for helpful discussions concerning Theorem 3.1 and other valuable comments. Moreover, the author is grateful to Professor H. P. Benson and three referees for valuable remarks and suggestions concerning a previous draft of this paper.     

Constraint qualifications in multiobjective optimization problems: Differentiable case

In this paper, we are concerned with a multiobjective optimization problem with inequality constraints. We introduce a constraint qualification and derive the Kuhn-Tucker type necessary conditions for efficiency. Moreover, we give conditions which ensure the constraint qualification.This work was done while the author was visiting the University of California, Berkeley, California.     

期望和残差收益估计不可靠的鲁棒模型

投资优化问题的最优策略会随着输入参数的扰动而出现敏感的变化,针对投资优化问题中出现的随机变量的参数估计不可靠的情况,本文引入不确定集合描述随机收益的有关矩信息,提出了投资优化问题的一个鲁棒性模型,并采用数学规划的理论和方法,给出了该模型的最优策略和有效前沿的解析表示。本方法能够为采用保守策略的、对不确定性厌恶的投资者提供一种最优的投资策略。     

多分散高浓度介质偏振光后向扩散散射的Monte Carlo仿真

建立了针对多分散高浓度介质偏振光后向扩散散射的Monte Carlo仿真模型，导出了多分散 系统的有效自由程分布函数. 给出了半径为50nm与550nm及其三种不同体积浓度比混合的聚 苯乙烯微球作为散射粒子的高浓度介质的仿真结果. 定性地分析了多分散介质偏振光后向扩 散散射的光强空间分布特征与粒子的体积浓度比的关系. 关键词： 后向扩散散射 偏振光 多分散高浓度介质 Monte Carlo仿真     

Unbounded Components in the Solution Sets of Strictly Quasiconcave Vector Maximization Problems

Let (P) denote the vector maximization problem