A variant of the Topkis-Veinott method for solving inequality constrained optimization problems

J. R. Birge, Liqun Qi, Z. Wei

Research output: Journal article publicationJournal articleAcademic researchpeer-review

12 Citations (Scopus)

Abstract

In this paper we give a variant of the Topkis-Veinott method for solving inequality constrained optimization problems. This method uses a linearly constrained positive semidefinite quadratic problem to generate a feasible descent direction at each iteration. Under mild assumptions, the algorithm is shown to be globally convergent in the sense that every accumulation point of the sequence generated by the algorithm is a Fritz-John point of the problem. We introduce a Fritz-John (FJ) function, an FJ1 strong second-order sufficiency condition (FJ1-SSOSC), and an FJ2 strong second-order sufficiency condition (FJ2-SSOSC), and then show, without any constraint qualification (CQ), that (i) if an FJ point z satisfies the FJ1-SSOSC, then there exists a neighborhood N(z) of z such that, for any FJ point y ∈ N(z)\{z}, f0(y) ≠ f0(z), where f0is the objective function of the problem; (ii) if an FJ point z satisfies the FJ2-SSOSC, then z is a strict local minimum of the problem. The result (i) implies that the entire iteration point sequence generated by the method converges to an FJ point. We also show that if the parameters are chosen large enough, a unit step length can be accepted by the proposed algorithm.
Original languageEnglish
Pages (from-to)309-330
Number of pages22
JournalApplied Mathematics and Optimization
Volume41
Issue number3
DOIs
Publication statusPublished - 1 Jan 2000
Externally publishedYes

Keywords

  • Constrained optimization
  • Feasibility
  • Global convergence
  • Stochastic programming
  • Unit step

ASJC Scopus subject areas

  • Control and Optimization
  • Applied Mathematics

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