Abstract
In this paper, we introduce and study the Slater constraint qualification (CQ) for a semi-infinite optimization problem with upper-semicontinuous quasiconvex objective and constraint functions. Then, some Karush–Kuhn–Tucker (KKT) type necessary and sufficient optimality conditions as well as duality results are derived. The final part of the paper is devoted to a linear characterization of optimality and the gap function for considered semi-infinite problem.
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