A generalized karush-kuhn-tucki optimality condition without constraint qualification using tl approximate subdifferential

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.

Keywords:

• Karush-Kuhn-Tucker Optimality Conditions
• Non-smooth Analysis
• Nondifferentiable Programming
• Fritz John Optimality Conditions
• Concave Minimization
• Stochastic Programming
• AMS (1991) Subject Classification: 90C30
• 49J52
• 26E20