Partially strictly monotone and nonlinear penalty functions for constrained mathematical programs

Xiaoqi Yang, X. X. Huang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

5 Citations (Scopus)

Abstract

We introduce the concept of partially strictly monotone functions and apply it to construct a class of nonlinear penalty functions for a constrained optimization problem. This class of nonlinear penalty functions includes some (nonlinear) penalty functions currently used in the literature as special cases. Assuming that the perturbation function is lower semi-continuous, we prove that the sequence of optimal values of nonlinear penalty problems converges to that of the original constrained optimization problem. First-order and second-order necessary optimality conditions of nonlinear penalty problems are derived by converting the optimality of penalty problems into that of a smooth constrained vector optimization problem. This approach allows for a concise derivation of optimality conditions of nonlinear penalty problems. Finally, we prove that each limit point of the second-order stationary points of the nonlinear penalty problems is a second-order stationary point of the original constrained optimization problem.
Original languageEnglish
Pages (from-to)293-311
Number of pages19
JournalComputational Optimization and Applications
Volume25
Issue number1-3
DOIs
Publication statusPublished - 1 Apr 2003

Keywords

  • Constrained mathematical program
  • Convergence analysis
  • Nonlinear penalty function
  • Optimality condition
  • Partially strictly monotone function

ASJC Scopus subject areas

  • Control and Optimization
  • Computational Mathematics
  • Applied Mathematics

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