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Optimality conditions of fenchel-lagrange duality and farkas-type results for composite dc infinite programs

  • *Corresponding author

    *Corresponding author 

This work was supported by the Natural Science Foundation of China (11401533), the Zhejiang Provincial Natural Science Foundation of China (LY18A010030), the Scientific Research Fund of Zhejiang Provincial Education Department (19060042-F) and the Science Foundation of Zhejiang Sci-Tech University (19062150-Y)

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  • This paper is concerned with a DC composite programs with infinite DC inequalities constraints. Without any topological assumptions and generalized increasing property, we first construct some new regularity conditions by virtue of the epigraph technique. Then we give some complete characterizations of the (stable) Fenchel-Lagrange duality and the (stable) Farkas-type assertions. As applications, corresponding assertions for the DC programs with infinite inequality constraints and the conic programs with DC composite function are also given.

    Mathematics Subject Classification: Primary: 90C26, 90C30; Secondary: 90C46.

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