Duality theorems and an optimality condition for non-differentiable convex programming
- 1 June 1982
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics
- Vol. 32 (3) , 369-379
- https://doi.org/10.1017/s1446788700024927
Abstract
Necessary and sufficient optimality conditions of Kuhn-Tucker type for a convex programming problem with subdifferentiable operator constraints have been obtained. A duality theorem of Wolfe's type has been derived. Assuming that the objective function is strictly convex, a converse duality theorem is obtained. The results are then applied to a programming problem in which the objective function is the sum of a positively homogeneous, lower-semi-continuous, convex function and a continuous convex function.Keywords
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