Robust Stability and Optimality Conditions for Parametric Infinite and Semi-Infinite Programs

摘要: This paper primarily concerns the study of parametric problems infinite and semi-infinite programming, where functional constraints are given by systems infinitely many linear inequalities indexed an arbitrary set T, decision variables run over Banach (infinite programming) or finite-dimensional (semi-infinite case) spaces, objectives generally described nonsmooth nonconvex cost functions. The parameter space admissible perturbations in such is formed all bounded functions on T equipped with standard supremum norm. Unless index finite, this intrinsically infinite-dimensional (nonreflexive nonseparable) l=-type. By using advanced tools variational analysis generalized differentiation largely exploiting underlying specific features constraints, we establish complete characterizations robust Lipschitzian stability (with computing exact bound moduli) for maps feasible solutions governed inequality then derive verifiable necessary optimality conditions programs under consideration expressed terms their initial data. A crucial part our addresses precise computation coderivatives norms general spaces variables. results obtained new both frameworks programming.