Slater CQ, optimality and duality for quasiconvex semi-infinite optimization problems

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.