论文标题
强大的矢量平衡问题的一些增强的存在结果
Some enhanced existence results for strong vector equilibrium problems
论文作者
论文摘要
本文探讨了一些足够的条件，以增强强矢量平衡问题的可溶性，这可以通过变异方法确定。此处增强的可解决性意味着解决方案的存在，这些解决方案相对于部分有序，辅以估计与溶液集距离的不平等（即误差界）。这种估计值在解决方案集的切向（一阶）近似以及用平衡约束（MPEC）的数学编程的最佳条件中起着至关重要的作用。 此处遵循的方法将解决方案描述为与原始问题相关的某些优点功能的零（或全局最小化）。因此，为了达到主要结果，KKM理论的传统就业被绩效功能的斜率上的适当条件所取代。反过来，为了使这种情况可验证，利用了一些非平滑分析工具。结果，得出了一些强大平衡问题的可溶性的条件，这些条件是根据广义（Bouligand）衍生物，凸正常的和各种（Fenchel和Mordukhovich）亚分差表示的。
This paper explores some sufficient conditions for the enhanced solvability of strong vector equilibrium problems, which can be established via a variational approach. Enhanced solvability here means existence of solutions, which are strong with respect to the partial ordering, complemented with inequalities estimating the distance from the solution set (namely, error bounds). This kind of estimates plays a crucial role in the tangential (first-order) approximation of the solution set as well as in formulating optimality conditions for mathematical programming with equilibrium constraints (MPEC). The approach here followed characterizes solutions as zeros (or global minimizers) of some merit functions associated to the original problem. Thus, to achieve the main results the traditional employment of the KKM theory is replaced by proper conditions on the slope of the merit functions. In turn, to make such conditions verifiable, some tools of nonsmooth analysis are exploited. As a result, several conditions for the enhanced solvability of strong equilibrium problems are derived, which are expressed in terms of generalized (Bouligand) derivatives, convex normals and various (Fenchel and Mordukhovich) subdifferentials.
