Successive Optimization Method via Parametric Monotone Composition Formulation

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4 Citations (Scopus)

Abstract

In this paper a successive optimization method for solving inequality constrained optimization problems is introduced via a parametric monotone composition reformulation. The global optimal value of the original constrained optimization problem is shown to be the least root of the optimal value function of an auxiliary parametric optimization problem, thus can be found via a bisection method. The parametric optimization subproblem is formulated in such a way that it is a one-parameter problem and its value function is a monotone composition function with respect to the original objective function and the constraints. Various forms can be taken in the parametric optimization problem in accordance with a special structure of the original optimization problem, and in some cases, the parametric optimization problems are convex composite ones. Finally, the parametric monotone composite reformulation is applied to study local optimality.
Original languageEnglish
Pages (from-to)355-369
Number of pages15
JournalJournal of Global Optimization
Volume16
Issue number4
DOIs
Publication statusPublished - 1 Jan 2000

Keywords

  • Convexification
  • Global optimization
  • Least root problem
  • Optimality condition
  • Parametric monotone composition

ASJC Scopus subject areas

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

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