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Lagrangean conditions and quasiduality

Published online by Cambridge University Press:  17 April 2009

B.D. Craven
B.D. Craven
Affiliation:
Department of Mathematics, University of Melbourne, Parkville, Victoria.
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Abstract

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For a constrained minimization problem with cone constraints, lagrangean necessary conditions for a minimum are well known, but are subject to certain hypotheses concerning cones. These hypotheses are now substantially weakened, but a counter example shows that they cannot be omitted altogether. The theorem extends to minimization in a partially ordered vector space, and to a weaker kind of critical point (a quasimin) than a local minimum. Such critical points are related to Kuhn-Tucker conditions, assuming a constraint qualification; in certain circumstances, relevant to optimal control, such a critical point must be a minimum. Using these generalized critical points, a theorem analogous to duality is proved, but neither assuming convexity, nor implying weak duality.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 16 , Issue 3 , June 1977 , pp. 325 - 339
Copyright
Copyright © Australian Mathematical Society 1977

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