Perfect duality for convexlike programs

M. Hayashi, Hidetoshi Komiya

Research output: Contribution to journalArticle

50 Citations (Scopus)

Abstract

The minimizing problem for a convex program has a dual problem, that is, the maximizing problem of the Lagrangian. Although these problems have a duality gap in general, the duality gap can be eliminated by relaxing the constraint of the minimizing problem, so that the constraint is enforced only in the limit. We extend this result to the convexlike case. Moreover, we obtain a necessary condition for optimality for minimizing problems whose objective function and constraint mapping have convex Gateaux derivative.

Original languageEnglish
Pages (from-to)179-189
Number of pages11
JournalJournal of Optimization Theory and Applications
Volume38
Issue number2
DOIs
Publication statusPublished - 1982 Oct
Externally publishedYes

Fingerprint

Duality
Derivatives
Duality Gap
Gateaux Derivative
Convex Mapping
Convex Program
Dual Problem
Optimality
Objective function
Necessary Conditions
Dual problem

Keywords

  • Convexlike programs
  • Lagrangian function
  • necessary condition for optimality
  • perfect duality

ASJC Scopus subject areas

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

Cite this

Perfect duality for convexlike programs. / Hayashi, M.; Komiya, Hidetoshi.

In: Journal of Optimization Theory and Applications, Vol. 38, No. 2, 10.1982, p. 179-189.

Research output: Contribution to journalArticle

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