Duality theorems and an optimality condition for non-differentiable convex programming
P. Kanniappan, S. Sastry · Journal of the Australian Mathematical Society Series A Pure Mathematics and Statistics · 1982
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.