Abstract
ABSTRACTThe 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.
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