A unified gradient flow approach to constrained nonlinear optimization problems

S. Wang, Xiaoqi Yang, K. L. Teo

Research output: Journal article publicationJournal articleAcademic researchpeer-review

12 Citations (Scopus)

Abstract

This paper presents a unified gradient flow approach to nonlinear constrained optimization problems. This method is based on a continuous gradient flow reformulation of constrained optimization problems and on a two level time discretization of the gradient flow equation with a splitting parameter θ. The convergence of the scheme is analyzed and it is shown that the scheme becomes first order when θ ∈ [0, 1] and second order when θ = 1 and the time discretization step length is sufficiently large. Numerical experiments for continuous, discrete and mixed discrete optimization problems were performed, and the numerical results show that the approach is effective for solving these problems.
Original languageEnglish
Pages (from-to)251-268
Number of pages18
JournalComputational Optimization and Applications
Volume25
Issue number1-3
DOIs
Publication statusPublished - 1 Apr 2003

Keywords

  • Convergence analysis
  • Discretization method
  • Gradient flow
  • Nonlinear optimization problem

ASJC Scopus subject areas

  • Applied Mathematics
  • Control and Optimization
  • Management Science and Operations Research
  • Computational Mathematics

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