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.
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Dontchev, A.L. 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 98, 467–473 (1998). https://doi.org/10.1023/A:1022649803808
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DOI: https://doi.org/10.1023/A:1022649803808