A general framework for convex relaxation of polynomial optimization problems over cones

Masakazu Kojima, Sunyoung Kim, Hayato Waki

Research output: Contribution to journalArticle

22 Citations (Scopus)

Abstract

The class of POPs (Polynomial Optimization Problems) over cones covers a wide range of optimization problems such as 0-1 integer linear and quadratic programs, nonconvex quadratic programs and bilinear matrix inequalities. This paper presents a new framework for convex relaxation of POPs over cones in terms of linear optimization problems over cones. It provides a unified treatment of many existing convex relaxation methods based on the lift-and-project linear programming procedure, the reformulation-linearization technique and the semidefinite programming relaxation for a variety of problems. It also extends the theory of convex relaxation methods, and thereby brings flexibility and richness in practical use of the theory.

Original languageEnglish
Pages (from-to)125-144
Number of pages20
JournalJournal of the Operations Research Society of Japan
Volume46
Issue number2
DOIs
Publication statusPublished - Jun 2003

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Optimization problem
Polynomials
Integer
Linearization
Semidefinite programming
Linear programming

All Science Journal Classification (ASJC) codes

  • Decision Sciences(all)
  • Management Science and Operations Research

Cite this

A general framework for convex relaxation of polynomial optimization problems over cones. / Kojima, Masakazu; Kim, Sunyoung; Waki, Hayato.

In: Journal of the Operations Research Society of Japan, Vol. 46, No. 2, 06.2003, p. 125-144.

Research output: Contribution to journalArticle

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