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Stable Strong Duality for Composed Optimization Problems with Composed Constraints
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Abstract
This paper is devoted to the study of stable strong duality for composed convex optimization problems with composed constraints. To this end, we establish generalized Farkas-type results and provide characterizations for inequality systems involving composed convex functions under composed constraints. These results extend several existing results in convex and nonconvex programming. In particular, we introduce a sufficient condition ensuring generalized Farkas-type results in the composite setting. The obtained results are then applied to derive strong and stable strong duality for composed convex optimization problems with composed constraints, as well as optimality conditions for the aforementioned problem. As illustrations of the results, we present some consequences and applications to special cases.
Keywords
stable strong duality, composed convex optimization problems, Farkas-type results, optimality conditions, DC programs
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References
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