We prove that if a second order sufficient condition and a constraint regularity assumption hold, then for sufficiently small perturbations of the constraints and the objective function, the set of local minimizers reduces to a singleton. Moreover, the minimizes and the associated multipliers are Lipschitzian functions of the parameter.
This is the publisher's version, also available electronically from http://epubs.siam.org/doi/abs/10.1137/0324068.
Cornet, Bernard; Vial, Jean-Phillippe. (1986). "Lipschitzian Solutions of Perturbed Nonlinear Programming Problems." SIAM Journal of Control and Optimization, 24(6):1123-1137. http://www.dx.doi.org/10.1137/0324068
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