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Optimality conditions and duality for semi-infinite programming involving B-arcwise connected functions

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Abstract

In this paper, a class of functions called B-arcwise connected (BCN) and strictly B-arcwise connected (STBCN) functions are introduced by relaxing definitions of arcwise connected function (CN) and B-vex function. The differential properties of B-arcwise connected function (BCN) are studied. Their two extreme properties are proved. The necessary and sufficient optimality conditions are obtained for the nondifferentiable nonlinear semi-infinite programming involving B-arcwise connected (BCN) and strictly B-arcwise connected (STBCN) functions. Mond-Weir type duality results have also been established.

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Authors and Affiliations

  1. College of Mathematics and Computer Science, Yanan University, Yanan Shaanxi, 716000, People’s Republic of China

    Qingxiang Zhang

  2. Institute of Mathematics, Yanan University, Yanan Shaanxi, 716000, People’s Republic of China

    Qingxiang Zhang

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  1. Qingxiang Zhang
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Correspondence to Qingxiang Zhang.

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Zhang, Q. Optimality conditions and duality for semi-infinite programming involving B-arcwise connected functions. J Glob Optim 45, 615–629 (2009). https://doi.org/10.1007/s10898-009-9400-8

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  • DOI: https://doi.org/10.1007/s10898-009-9400-8

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