Contractibility of Efficient Frontier of Simply Shaded Sets

In finite dimensional Euclidean space, we prove the contractibility of the efficient frontier of simply shaded sets. This work extends the result of Peleg [7], which confirms the contractibility of the efficient frontier in the convex case.     

向量优化问题广义有效点的一个存在性定理

利用集值映射不动点定理及最优化问题与变分不等式的关系给出线性G^↑ateaux可微的锥凸映射的广义有效点的一个存在性定理。     

多目标规划的鞍点准则

本文给出多目标规划有效解适应鞍点准则的一个新的判别法 ,它不使用凸性的几何术语及凸分析中的概念。最后给出单目标规划的一个相应的判别法     

On the existence of efficient points in locally convex spaces

We study the existence of efficient points in a locally convex space ordered by a convex cone. New conditions are imposed on the ordering cone such that for a set which is closed and bounded in the usual sense or with respect to the cone, the set of efficient points is nonempty and the domination property holds.     

Proper efficiency and duality for a class of constrained multiobjective fractional optimal control problems containing arbitrary norms

We establish necessary and sufficient conditions for properly efficient solutions of a class of nonsmooth nonconvex optimal control problems with multiple fractional objective functions, linear dynamics, and nonlinear inequality constraints on both the state and control variables. Subsequently, we utilize these proper efficiency criteria to construct two multiobjective dual problems and prove appropriate duality theorems. Also, we specialize and discuss these results for a particular case of our principal problem which contains square roots of positivesemidefinite quadratic forms. As special cases of the main proper efficiency and duality results, this paper also contains similar results for control problems with multiple, fractional, and ordinary objective functions.     

Finding efficient solutions for rectilinear distance location problems efficiently

Given n planar existing facility locations, a planar new facility location X is called efficient if there is no other location Y for which the rectilinear distance between Y and each existing facility is at least as small as between X and each existing facility, and strictly less for at least one existing facility. Rectilinear distances are typically used to measure travel distances between points via rectilinear aisles or street networks. We first present a simple arrow algorithm, based entirely on geometrical analysis, that constructs all efficient locations. We then present a row algorithm which is of order n(log n) that constructs all efficient locations, and establish that no alternative algorithm can be of a lower order.     

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

Let (P) denote the vector maximization problem

On proper and improper efficient solutions of optimal problems with multicriteria

The properness of the efficient solution of the optimal problem with multicriteria has been independently defined by Kuhn and Tucker, Geoffrion, and Klinger. A theorem of Geoffrion describes the relation between Geoffrion's and Kuhn and Tucker's properness. In this paper, the dual part of the theorem is given, and some geometric approach is applied to derive the optimal conditions of proper efficient solutions and improper efficient solutions.     

Admissible points of a convex polyhedron

In this paper, we present several new properties of the admissible points of a convex polyhedron. These properties can be classified into two categories. One category concerns the characterization and generation of these points. The other category concerns the circumstances under which these points are efficient solutions for linear multiple-objective programs with nonnegative criteria matrices. To illustrate some of the potential utility of these properties, we describe their application to two practical problems. These problems are the linear multiple-objective problem with interval coefficients and the problem of optimizing over the efficient set.This research was supported, in part, by the Center for Econometrics and Decision Sciences, University of Florida, Gainesville, Florida.