A Limiting Lagrangean for Infinitely-Constrained Convex Optimization in Rn.
Management sciences research rept.,
CARNEGIE-MELLON UNIV PITTSBURGH PA MANAGEMENT SCIENCES RESEARCH GROUP
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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.
- Theoretical Mathematics