Suboptimal control over semilinear elliptic equations with phase constraints. II: Sensitivity, typicalness of the regular maximum principle
The paper considers on optimal control problem governed by a semilinear elliptic equation with additional state constraints of the type \(y\in M+ q\subset C(Q)\), where \(Q\) is a compact subset of the reference domain \(\Omega\), \(M\) is a convex closed set with nonempty interior and \(q\) is a parameter. Necessary conditions which must satisfy approximating (with respect to the state constraints) minimizing sequences are given, and continuity properties (with respect to the parameter \(q\)) of the value of the problem are investigated. For Part I see [\textit{M. I. Sumin}, Russ. Math. 44, No. 6, 31-42 (2000); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2000, No. 6, 33-44 (2000; Zbl 1003.49020)].
necessary conditions for minimizing sequences
scientific article; zbMATH DE number 1758688