General constraint qualifications in nondifferentiable programming |
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Authors: | R R Merkovsky D E Ward |
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Institution: | (1) Department of Mathematical Sciences, Purdue University Calumet, 46323 Hammond, IN, USA;(2) Department of Mathematics and Statistics, Miami University, 45056-1641 Oxford, OH, USA |
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Abstract: | We 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. |
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Keywords: | Constraint qualification tangent cone directional derivative subgradient upper convex approximate nondifferentiable programming |
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