Stable extensions of constrained optimization problems
Using ``language'' and methods of proximity spaces [see, e.g., \textit{S. A. Naimpally} and \textit{B. D. Warrack}, Proximity spaces (1970; Zbl 0206.246)] a parameter-dependent optimization problem with inequality constraints is extended in such a way, that under conditions (which are weaker than those of known theorems, corresponding to this topic) marginal functions (e.g. the optimal value function) are in a well- defined sense continuous. The classical marginal functions do not have such stability properties. The above mentioned extension is in some sense a most general one. The results are supported by earlier papers of the author [Kybernetika 22, 289-298 (1986; Zbl 0626.49013); SIAM J. Control Optimization 24, 951- 960 (1986; Zbl 0603.90137)].
parameter-dependent optimization problem
scientific article; zbMATH DE number 4119067
scientific article