Mathematical Programming

, Volume 47, Issue 1–3, pp 389–405 | Cite as

General constraint qualifications in nondifferentiable programming

  • R. R. Merkovsky
  • D. E. Ward


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.

Key words

Constraint qualification tangent cone directional derivative subgradient upper convex approximate nondifferentiable programming 


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Copyright information

© The Mathematical Programming Society, Inc. 1990

Authors and Affiliations

  • R. R. Merkovsky
    • 1
  • D. E. Ward
    • 2
  1. 1.Department of Mathematical SciencesPurdue University CalumetHammondUSA
  2. 2.Department of Mathematics and StatisticsMiami UniversityOxfordUSA

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