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Necessary Conditions for Weak Sharp Minima in Cone‐Constrained Optimization Problems

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  • W. Y. Zhang
  • S. Xu
  • S. J. Li

Abstract

We study weak sharp minima for optimization problems with cone constraints. Some necessary conditions for weak sharp minima of higher order are established by means of upper Studniarski or Dini directional derivatives. In particular, when the objective and constrained functions are strict derivative, a necessary condition is obtained by a normal cone.

Suggested Citation

  • W. Y. Zhang & S. Xu & S. J. Li, 2012. "Necessary Conditions for Weak Sharp Minima in Cone‐Constrained Optimization Problems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:909520
    DOI: 10.1155/2012/909520
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    References listed on IDEAS

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    1. Jim Burke & S.-P. Han, 1986. "A Gauss-Newton Approach to Solving Generalized Inequalities," Mathematics of Operations Research, INFORMS, vol. 11(4), pages 632-643, November.
    2. Joseph Frédéric Bonnans & Alexander Ioffe, 1995. "Second-order Sufficiency and Quadratic Growth for Nonisolated Minima," Mathematics of Operations Research, INFORMS, vol. 20(4), pages 801-817, November.
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