A penalty approximation method for a semilinear parabolic double obstacle problem

Y. Y. Zhou, S. Wang, Xiaoqi Yang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

11 Citations (Scopus)

Abstract

In this work, we present a novel power penalty method for the approximation of a global solution to a double obstacle complementarity problem involving a semilinear parabolic differential operator and a bounded feasible solution set. We first rewrite the double obstacle complementarity problem as a double obstacle variational inequality problem. Then, we construct a semilinear parabolic partial differential equation (penalized equation) for approximating the variational inequality problem. We prove that the solution to the penalized equation converges to that of the variational inequality problem and obtain a convergence rate that is corresponding to the power used in the formulation of the penalized equation. Numerical results are presented to demonstrate the theoretical findings.
Original languageEnglish
Pages (from-to)531-550
Number of pages20
JournalJournal of Global Optimization
Volume60
Issue number3
DOIs
Publication statusPublished - 1 Jan 2014

Keywords

  • Complementarity problem
  • Double obstacle problem
  • Global optimizer
  • Parabolic differential operator
  • Penalty approximation method

ASJC Scopus subject areas

  • Computer Science Applications
  • Control and Optimization
  • Management Science and Operations Research
  • Applied Mathematics

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