鲁棒凸优化问题拟近似解的刻划

Characterizations of Quasi Approximate Solution for RobustConvex Optimization Problems

本文研究鲁棒凸优化问题拟近似解的最优性条件和对偶理论.首先利用鲁棒优化方法,在由约束函数的共轭函数的上图给出的闭凸锥约束规格条件下,建立了拟近似解的最优性充要条件.其次给出了鲁棒凸优化问题拟近似解在Wolf型和Mond-weir型对偶模型下的强(弱)对偶定理.最后给出具体实例验证了本文获得的结果.

In this paper,we study quasi approximate solution for a robust convex optimization problem in the face of data uncertainty.By using the robust optimization approach,we first establish optimality conditions for quasi approximate solution under a closed convex cone constraint qualification which is given by conjugate function for the constraint function.In addition,we also characterizeWolf type and Mond-weir type duality theorems for quasi approximate solution on the robust convex optimization problem.Moreover,some examples are given to illustrate the obtained results.