Journal of Optimization Theory and Applications

, Volume 67, Issue 1, pp 87–108

Zero duality gaps in infinite-dimensional programming

Authors

  • V. Jeyakumar
    • Department of Applied MathematicsUniversity of New South Wales
  • H. Wolkowicz
    • Department of Combinatorics and OptimizationUniversity of Waterloo
Contributed Papers

DOI: 10.1007/BF00939737

Cite this article as:
Jeyakumar, V. & Wolkowicz, H. J Optim Theory Appl (1990) 67: 87. doi:10.1007/BF00939737

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 gapsconvex-like infinite programsvalue functionsemi-infinite programmingsubdifferentiability

Copyright information

© Plenum Publishing Corporation 1990