Verification of second-order sufficient optimality conditions for semilinear elliptic and parabolic control problems

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6 Scopus citations

Abstract

We study optimal control problems for semilinear parabolic equations subject to control constraints and for semilinear elliptic equations subject to control and state constraints. We quote known second-order sufficient optimality conditions (SSC) from the literature. Both problem classes, the parabolic one with boundary control and the elliptic one with boundary or distributed control, are discretized by a finite difference method. The discrete SSC are stated and numerically verified in all cases providing an indication of optimality where only necessary conditions had been studied before.

Original languageEnglish (US)
Pages (from-to)93-110
Number of pages18
JournalComputational Optimization and Applications
Volume20
Issue number1
DOIs
StatePublished - Oct 1 2001

Keywords

  • Control and state constraints
  • Discretizations
  • Elliptic and parabolic control problems
  • Optimization methods
  • Second-order sufficient conditions

ASJC Scopus subject areas

  • Control and Optimization
  • Computational Mathematics
  • Applied Mathematics

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