Optimality conditions and total dualities for conic programming involving composite function. (1st February 2020) - Fang, Donghui; Zhang, Yong
ABSTRACT: The paper concerns the study of a new class of conic programming with objectives given as the difference of a composite function and a convex function. We first introduce two new notions of regularity conditions in terms of the subdifferential of the involving functions. Under the new regularity conditions, we provide some necessary and/or sufficient conditions for KKT type optimality conditions to hold. Similarly, saddle point theorems and total Lagrange dualities for conic programming are also given.