A note on nondifferentiable symmetric duality
Craven, B. D.; Craven B. D.; Univerisity of Melbourne
Журнал:
The Journal of the Australian Mathematical Society. Series B. Applied Mathematics
Дата:
1986
Аннотация:
Under suitable hypotheses on the function f, the two constrained minimization problems:are well known each to be dual to the other. This symmetric duality result is now extended to a class of nonsmooth problems, assuming some convexity hypotheses. The first problem is generalized to:in which T and S are convex cones, S* is the dual cone of S, and ∂<sub>y</sub> denotes the subdifferential with respect to y. The usual method of proof uses second derivatives, which are no longer available. Therefore a different method is used, where a nonsmooth problem is approximated by a sequence of smooth problems. This duality result confirms a conjecture by Chandra, which had previously been proved only in special cases.
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