向量优化KKT乘子的有界性

Bounded Sets of KKT Multipliers in Vector Optimization

考虑具有等式约束和不等式约束的抽象多目标优化问题.主要证明了在基本正则条件的假设下向量优化存在一个非空、有界的KKT真乘子集.假设目标函数和约束函数都是光滑的.首先定义了向量优化的基本正则条件.其次,证明了常量优化问题KKT乘子的存在性.最后,把常量优化扩展到向量优化中,证明了在基本正则条件和Pareto最小或Pareto弱最小情形下向量优化的真KKT乘子的有界性.

In this paper, we consider the multiobjective optimization problem that incorporates not only equality constraints but also inequality constraints. Mainly proves that under the assumption of the condition of basic regular vector optimization is a non-empty, bounded KKT true subset. We assume that the objective function and constraint functions are smooth. First of all, defines the basic regular condition of vector optimization. Secondly, proves the existence of constant optimization problem KKT multipliers. Finally, expand the constant optimization of vector optimization, proved in the basic conditions of regular and Pareto minimum or Pareto weak minimum case vector optimization of true KKT multipliers boundedness.