ON $\epsilon$-APPROXIMATE SOLUTIONS FOR CONVEX SEMIDEFINITE OPTIMIZATION PROBLEMS

Abstract

In this paper, we discuss $\epsilon$-optimality conditions and $\epsilon$-saddle point theorems for $\epsilon$-approximate solutions for convex semidefinite optimization problem which hold under a weakened constraint qualification or which hold without any constraint qualification.

Moreover, we formulate a Wolfe type dual problem for the convex semidefinite optimization problem, and prove $\epsilon$-weak duality and $\epsilon$-strong duality between the primal problem and the dual problem, which hold under a weakened constraint qualification.