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A Proof of the Necessity of Linear Independence Condition and Strong Second-Order Sufficient Optimality Condition for Lipschitzian Stability in Nonlinear Programming

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  • A. L. Dontchev

    (Mathematical Reviews)

Abstract

For a nonlinear programming problem with a canonical perturbations, we give an elementary proof of the following result: If the Karush–Kuhn–Tucker map is locally single-valued and Lipschitz continuous, then the linear independence condition for the gradients of the active constraints and the strong second-order sufficient optimality condition hold.

Suggested Citation

  • A. L. Dontchev, 1998. "A Proof of the Necessity of Linear Independence Condition and Strong Second-Order Sufficient Optimality Condition for Lipschitzian Stability in Nonlinear Programming," Journal of Optimization Theory and Applications, Springer, vol. 98(2), pages 467-473, August.
    • Handle: RePEc:spr:joptap:v:98:y:1998:i:2:d:10.1023_a:1022649803808
    DOI: 10.1023/A:1022649803808
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    References listed on IDEAS

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    1. CORNET, Bernard & LAROQUE, Guy, 1987. "Lipschitz properties of solutions in mathematical programming," LIDAM Reprints CORE 847, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Stephen M. Robinson, 1980. "Strongly Regular Generalized Equations," Mathematics of Operations Research, INFORMS, vol. 5(1), pages 43-62, February.
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    Cited by:

    1. Daniel L. McFadden & Mogens Fosgerau, 2012. "A theory of the perturbed consumer with general budgets," NBER Working Papers 17953, National Bureau of Economic Research, Inc.

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