Journal of Optimization Theory and Applications

, Volume 67, Issue 1, pp 87–108

Zero duality gaps in infinite-dimensional programming

  • V. Jeyakumar
  • H. Wolkowicz
Contributed Papers

Abstract

In this paper we study the following infinite-dimensional programming problem: (P) μ≔inff0(x), subject toxC,fi(x)≤0,iI, whereI is an index set with possibly infinite cardinality andC is an infinite-dimensional set. Zero duality gap results are presented under suitable regularity hypotheses for convex-like (nonconvex) and convex infinitely constrained program (P). Various properties of the value function of the convex-like program and its connections to the regularity hypotheses are studied. Relationships between the zero duality gap property, semicontinuity, and ε-subdifferentiability of the value function are examined. In particular, a characterization for a zero duality gap is given, using the ε-subdifferential of the value function without convexity.

Key Words

Zero duality gaps convex-like infinite programs value function semi-infinite programming subdifferentiability 

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Copyright information

© Plenum Publishing Corporation 1990

Authors and Affiliations

  • V. Jeyakumar
    • 1
  • H. Wolkowicz
    • 2
  1. 1.Department of Applied MathematicsUniversity of New South WalesKensingtonAustralia
  2. 2.Department of Combinatorics and OptimizationUniversity of WaterlooWaterlooCanada

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