Abstract
The perturbation theory for the standard nonlinear programming problem (finite dimensional setting, finite number of constraints, smooth data) has made decisive progress in the very recent years. Gauvin and Janin (1988, 1989) gave a formula for the derivative of the solutions under the hypotheses of standard second order sufficient condition and a (weak) directional qualification hypothesis due to Gollan (1981). Shapiro (1988) made the second-order analysis of the cost and obtained the first term in the expansion of the solutions, under a strengthened second-order condition and the Mangasarian-Fromovitz (MF) hypothesis. Auslender and Cominetti (1990) extended his results replacing (MF) by the directional qualification hypothesis.
The second author was suported in part by the Fund of Promotion of Science at the Technion under the Grant 100-820.
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© 1992 Springer-Verlag Berlin Heidelberg
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Bonnans, J.F., Ioffe, A.D., Shapiro, A. (1992). Expansion of exact and approximate solutions in nonlinear programming. In: Oettli, W., Pallaschke, D. (eds) Advances in Optimization. Lecture Notes in Economics and Mathematical Systems, vol 382. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-51682-5_8
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DOI: https://doi.org/10.1007/978-3-642-51682-5_8
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