ϵ-Duality Theorems for Convex Semidefinite Optimization Problems with Conic Constraints

Abstract

A convex semidefinite optimization problem with a conic constraint is considered. We formulate a Wolfe-type dual problem for the problem for its ϵ-approximate solutions, and then we prove ϵ-weak duality theorem and ϵ-strong duality theorem which hold between the problem and its Wolfe type dual problem. Moreover, we give an example illustrating the duality theorems.