We show that a compact feasible set of a standard semi-infinite optimization problem can be approximated arbitrarily well by a level set of a single smooth function with certain regularity properties. This function is constructed as the mollification of the lower level optimal value function. Moreover, we use correspondences between KarushKuhn-Tucker points of the original and the smoothed prob...

The characteristic asymptotic fields at the tip of sharp, semi-infinite cracks and notches are first compared with corresponding features present in selected finite bodies (edge cracks and notches). This gives an explicit view of the gradual divergence of the semiinfinite and finite problem solutions as the observation point becomes remote from the tip. Hence, upper bounds for the local plastic...

This paper is devoted to the study of the stability of the solution map for the parametric convex semi-infinite optimization problem under convex function perturbations in short, PCSI. We establish sufficient conditions for the pseudo-Lipschitz property of the solution map of PCSI under perturbations of both objective function and constraint set. The main result obtained is new even when the pr...

In a common formulation of semi-infinite programs, the infinite constraint set is a requirement that a function parametrized by the decision variables is nonnegative over an interval. If this function is sufficiently closely approximable by a polynomial or a rational function, then the semi-infinite program can be reformulated as an equivalent semidefinite program. Solving this semidefinite pro...