Regularity conditions characterizing Fenchel–Lagrange duality and Farkas-type results in DC infinite programming

Abstract In this paper, we consider a DC infinite programming problem ( P ) with inequality constraints. By using the properties of the epigraph of the conjugate functions, we introduce some new notions of regularity conditions for ( P ). Under these new regularity conditions, we completely characterize the Fenchel–Lagrange duality and the stable Fenchel–Lagrange duality for ( P ). Similarly, we also completely characterize the Farkas-type results and the stable Farkas-type results for ( P ). As applications, we obtain the corresponding results for conic programming problems.

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