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Locally compactly Lipschitzian mappings in infinite dimensional programming

Published online by Cambridge University Press:  17 April 2009

B.M. Glover
B.M. Glover
Affiliation:
School of Mathematics and Computing, Ballarat University College, Ballarat Vic 3353, Australia
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In this note we show that a subgradient multifunction of a locally compactly Lip-schitzian mapping satisfies a closure condition used extensively in optimisation theory. In addition we derive a chain rule applicable in either separable or reflexive Banach spaces for the class of locally compactly Lipschitzian mappings using a recently derived generalised Jacobian. We apply these results to the derivation of Karush-Kuhn-Tucker and Fritz John optimality conditions for general abstract cone-constrained programming problems. A discussion of constraint qualifications is undertaken in this setting.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 47 , Issue 3 , June 1993 , pp. 395 - 406
Copyright
Copyright © Australian Mathematical Society 1993

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