Applied Mathematics and Optimization

, Volume 39, Issue 2, pp 211–227

Second-Order Necessary Optimality Conditions for Some State-Constrained Control Problems of Semilinear Elliptic Equations

  • E. Casas
  • F. Tröltzsch

DOI: 10.1007/s002459900104

Cite this article as:
Casas, E. & Tröltzsch, F. Appl Math Optim (1999) 39: 211. doi:10.1007/s002459900104

Abstract.

In this paper we are concerned with some optimal control problems governed by semilinear elliptic equations. The case of a boundary control is studied. We consider pointwise constraints on the control and a finite number of equality and inequality constraints on the state. The goal is to derive first- and second-order optimality conditions satisfied by locally optimal solutions of the problem.

Key words. Boundary control, Semilinear elliptic equations, Optimality conditions, State constraints. AMS Classification. 49K20, 35J25. 

Copyright information

© 1999 Springer-Verlag New York Inc.

Authors and Affiliations

  • E. Casas
    • 1
  • F. Tröltzsch
    • 2
  1. 1.Departamento de Matemática Aplicada y Ciencias de la Computación, E.T.S.I. Industriales y de Telecomunicación, Universidad de Cantabria, Av. Los Castros s/n, 39071 Santander, Spain ES
  2. 2.Fakultät für Mathematik, Technische Universität Chemnitz, D-09107 Chemnitz, Germany DE

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