论文标题
一种新方案，用于近似弱有效的矢量有理优化问题集
A new scheme for approximating the weakly efficient solution set of vector rational optimization problems
论文作者
论文摘要
在本文中，我们提供了一个新方案，用于近似于有限的许多多项式不等式所定义的可行集合，以近似于弱有效的矢量优化问题设置的矢量优化问题。更确切地说，我们提出了一个程序，以获得所讨论问题的弱有效解决方案集的一系列明确近似值。每个近似值是单个多项式和可行集合的巨船集的相交。为此，我们利用与所考虑的问题相关的成就函数，并在从上方的可行设置上构造了它的多项式近似值。值得注意的是，构造可以转换为半决赛编程问题。几个非平凡的例子旨在说明拟议的新方案。
In this paper, we provide a new scheme for approximating the weakly efficient solution set for a class of vector optimization problems with rational objectives over a feasible set defined by finitely many polynomial inequalities. More precisely, we present a procedure to obtain a sequence of explicit approximations of the weakly efficient solution set of the problem in question. Each approximation is the intersection of the sublevel set of a single polynomial and the feasible set. To this end, we make use of the achievement function associated with the considered problem and construct polynomial approximations of it over the feasible set from above. Remarkably, the construction can be converted to semidefinite programming problems. Several nontrivial examples are designed to illustrate the proposed new scheme.
