Optimality conditions for a nondifferentiable minimax programming in complex spaces (Q1026081)

This paper deals with problems of the form \(\min_{\varsigma\in X}\max_{\eta\in Y}\text{Re}(f(\varsigma,\eta)+\langle Az,z\rangle^{1/2}),\) where \(X\) is the set of all \(\varsigma=(z,\bar{z})\in\mathbb{C}^{2n}\) for which a certain vector-valued function takes values in a prescribed polyhedral cone in \(\mathbb{C}^{p},\) \(Y\) is a given compact subset of \(\mathbb{C}^{2m},\) \(A\) is a positive semidefinite matrix and \(f=f(\varsigma,\eta)\) is a complex-valued continuous function which is analytic in the first variable. A set of necessary optimality conditions of the Kuhn-Tucker type is established, while sufficient optimality conditions are proved under additional assumptions involving generalized convexity.