Convexification, Concavification and Monotonization in Global Optimization

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

20 Scopus Citations
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Author(s)

  • D. Li
  • X. L. Sun
  • M. P. Biswal
  • F. Gao

Detail(s)

Original languageEnglish
Pages (from-to)213-226
Journal / PublicationAnnals of Operations Research
Volume105
Issue number1-4
Publication statusPublished - Jul 2001
Externally publishedYes

Abstract

We show in this paper that via certain convexification, concavification and monotonization schemes a nonconvex optimization problem over a simplex can be always converted into an equivalent better-structured nonconvex optimization problem, e.g., a concave optimization problem or a D.C. programming problem, thus facilitating the search of a global optimum by using the existing methods in concave minimization and D.C. programming. We first prove that a monotone optimization problem (with a monotone objective function and monotone constraints) can be transformed into a concave minimization problem over a convex set or a D.C. programming problem via pth power transformation. We then prove that a class of nonconvex minimization problems can be always reduced to a monotone optimization problem, thus a concave minimization problem or a D.C. programming problem.

Research Area(s)

  • Concave minimization, Concavification, Convexification, D.C. programming, Global optimization, Monotonic function, Monotonization

Citation Format(s)

Convexification, Concavification and Monotonization in Global Optimization. / Li, D.; Sun, X. L.; Biswal, M. P.; Gao, F.

In: Annals of Operations Research, Vol. 105, No. 1-4, 07.2001, p. 213-226.

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review