How to solve a semi-infinite optimization problem

After an introduction to main ideas of semi-infinite optimization, this article surveys recent developments in theory and numerical methods for standard and generalized semi-infinite optimization problems. Particular attention is paid to connections with mathematical programs with complementarity constraints, lower level Wolfe duality, semi-smooth approaches, as well as branch and bound techniques in adaptive convexification procedures. A section on recent genericity results includes a discussion of the symmetry effect in generalized semi-infinite optimization.

► We introduce main ideas of semi-infinite optimization.
► We surveys recent developments in theory and numerical methods for SIP and GSIP.
► Particular attention is paid to connections with MPCCs, lower level Wolfe duality, semi-smooth approaches, adaptive convexification.
► Recent genericity section includes a discussion of the symmetry effect in GSIP.