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

Authors:
Qingxiang Zhang
Affiliations:
College of Mathematics and Computer Science, Yanan University, Yanan Shaanxi, People's Republic of China 716000 and Institute of Mathematics, Yanan University, Yanan Shaanxi, People's Republic of ...
Venue:
Journal of Global Optimization
Year:
2009

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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.