非光滑半定规划的一阶最优性条件

摘要

首次考虑了非光滑半定规化问题.运用与非线性规划类似的技巧,把现存的理论扩展到约束是结构稀疏矩阵的情况,给出了其一阶最优性条件,考虑了严格互补条件不成立的情形.在约束矩阵为对角阵条件下,所用的正则条件与传统非线性优化意义下的是一致的.%This paper concerns nonsmooth semidefinite programming problems. We derive first-order optimality conditions analogous to those for nonlinear programming. Using techniques similar to those used in nonlinear programming, we extend existing theory to cover situations where the constraint matrix is structurally sparse. This discussion covers the case when strict complementarity dose not hold. The regularity conditions used are consistent with those of nonlinear programming in the sense that the conventional optimality conditions for nonlinear programming are obtained when the constraint matrix is diagonal.