General constraint qualifications in nondifferentiable programming

The authors show that a familiar constraint qualification of differentiable programming has ‘nonsmooth’ counterparts. As a result, necessary optimality conditions of Kuhn-Tucker type can be established for inequality-constrained mathematical programs involving functions not assumed to be differentiable, convex, or locally Lipschitzian. These optimality conditions reduce to the usual Karush-Kuhn-Tucker conditions in the differentiable case and sharpen previous results in the locally Lipschitzian case.