New dual constraint qualifications characterizing zero duality gaps of convex programs and semidefinite programs

摘要

In this paper, we present new dual constraint qualifications which completely characterize the zero duality gap property for convex programming problems in general Banach spaces. As an application, we derive constraint qualifications, characterizing zero duality gaps of semidefinite programs. Our approach makes use of convex majorants of support functions together with conjugate analysis and approximate subdifferentials of convex functions.