ISSN:
1573-2878
Keywords:
Lagrangians
;
nonlinear programming
;
Kuhn-Tucker theory
;
convex optimization
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract For convex optimization inR n,we show how a minor modification of the usual Lagrangian function (unlike that of the augmented Lagrangians), plus a limiting operation, allows one to close duality gaps even in the absence of a Kuhn-Tucker vector [see the introductory discussion, and see the discussion in Section 4 regarding Eq. (2)]. The cardinality of the convex constraining functions can be arbitrary (finite, countable, or uncountable). In fact, our main result (Theorem 4.3) reveals much finer detail concerning our limiting Lagrangian. There are affine minorants (for any value 0〈θ≤1 of the limiting parameter θ) of the given convex functions, plus an affine form nonpositive onK, for which a general linear inequality holds onR nAfter substantial weakening, this inequality leads to the conclusions of the previous paragraph. This work is motivated by, and is a direct outgrowth of, research carried out jointly with R. J. Duffin.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00935754
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