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On quasidifferentiable optimization

Published online by Cambridge University Press:  09 April 2009

B. D. Craven
B. D. Craven
Affiliation:
Mathematics Department, University of Melbourne, Parkville, Victoria, 3052, Australia
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Abstract

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Lagrangian necessary conditions for optimality, of both Fritz John and Kuhn Tucker types, are obtained for a constrained minimization problem, where the functions are locally Lipschitz and have directional derivatives, but need not have linear Gâteaux derivatives; the variable may be constrained to lie in a nonconvex set. The directional derivatives are assumed to have some convexity properties as functions of direction; this generalizes the concept of quasidifferentiable function. The convexity is not required when directional derivatives are replaced by Clarke generalized derivatives. Sufficient Kuhn Tucker conditions, and a criterion for the locally solvable constraint qualification, are obtained for directionally differentiable functions.

MSC classification

Secondary: 90C30: Nonlinear programming
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 41 , Issue 1 , August 1986 , pp. 64 - 78
Copyright
Copyright © Australian Mathematical Society 1986

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