A continuous method for convex programming problems

Lizhi LIAO*

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

8 Citations (Scopus)

Abstract

In this paper, we present a continuous method for convex programming (CP) problems. Our approach converts first the convex problem into a monotone variational inequality (VI) problem. Then, a continuous method, which includes both a merit function and an ordinary differential equation (ODE), is introduced for the resulting variational inequality problem. The convergence of the ODE solution is proved for any starting point. There is no Lipschitz condition required in our proof. We show also that this limit point is an optimal solution for the original convex problem. Promising numerical results are presented.

Original languageEnglish
Pages (from-to)207-226
Number of pages20
JournalJournal of Optimization Theory and Applications
Volume124
Issue number1
DOIs
Publication statusPublished - Jan 2005

Scopus Subject Areas

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

User-Defined Keywords

  • Continuous methods
  • Convex programming
  • Monotone variational inequalities

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