A Limiting Lagrangean for Infinitely-Constrained Convex Optimization in Rn.

Abstract

It is shown, for convex optimization in R superscript n, how a minor modification of the usual Lagrangean function plus a limiting operation, allows one to close duality gaps even in the absence of a Kuhn-Tucker vector. The cardinality of the convex constraining functions can be arbitrary (finite, countable, or uncountable). In fact, the main result reveals much finer detail concerning the Limiting Lagrangean. There are affine minorants (for any value 0 < theta is < or = to 1 of the limiting parameter theta) of the given convex functions, plus an affine form nonpositve on K, for which a general linear inequality holds on R superscript n.

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Document Details

Document Type
Technical Report
Publication Date
Apr 01, 1978
Accession Number
ADA055513

Entities

People

  • Robert G. Jeroslow

Organizations

  • Carnegie Mellon University

Tags

DTIC Thesaurus Topics

  • Algorithms
  • Convex Sets
  • Equations
  • Hypotheses
  • Inequalities
  • Military Research
  • New Jersey
  • Nonlinear Programming
  • Optimization
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  • Students
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  • Vector Spaces

Fields of Study

  • Mathematics

Readers

  • Mathematical Modeling and Probability Theory.
  • Operations Research
  • Statistical inference.