Min–sup-type zero duality gap properties for DC composite optimization problem

Abstract

Abstract In this paper, we present min–sup-type zero duality gap properties for DC composite optimization problem with conic constraints. Using properties of the subdifferentials of involved functions, we introduce some new constraint qualifications. Under these new constraint qualifications, we provide necessary and/or sufficient conditions for the min–sup-type stable zero duality to hold.

Keywords

• Zero duality gap property
• DC function
• Composite function
• Constraint qualification
• Conic programming