Structural stability in generalized semi-infinite optimization (Q2729340)

The article surveys the mathematics of generalized semi-infinite optimization as an application to the structural stability property. A wide class of optimization problems is considered under the boundedness assumption and qualification constraints for feasible sets. The author exposes theorems which are devoted to stability of the feasible sets in a suitable topological space and the structural stability property which makes it possible to identify various Kuhn--Tucker points. The author also discusses some aspects of optimal control for ordinary differential equations by studying the minimization problem and presents two approaches that describe the global structure and study the stability of the corresponding functional. The so-called characterizing theorem is proven and its possible generalizations are indicated.