1. Ballarat University College, School of Mathematics , Ballarat, Victoria, 3350, Australia;2. Department of Mathematics , University of Melbourne , Parkville, Victoria, 3052, Australia;3. University of Bergen , Bergen, 5008, Norway
Abstract:
A generalized Karush-Kuhn-Tucker first order optimality condition is established for an abstract cone-constrained programming problem involving locally Lipschitz functions using the approximate subdifferential. This result is obtained without recourse to a constraint qualification by imposing additional generalized convexity conditions on the constraint functions. A new Fritz John optimality condition is developed as a precursor to the main result. Several examples are provided to illustrate the results along with a discussion of applications to concave minimization problems and to stochastic programming problems with nonsmooth data.