Abstract
The implicit function theorem plays an important role in the stability and sensitivity analysis of optimization problems. In the last few years many authors obtained results in this sense, by using the implicit function theorem of Robinson (1980) (see e.g. Robinson (1980); Alt (1990), (1991); Ito-Kunish (1989); Malanowski (to appear)).
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References
Alt, W. (1990), The Lagrange-Newton method for infinite-dimensional optimization problems. Numer Funct Anal and Optimiz 11: 201–224
Alt, W. (1991), Parametric programming with application to optimal control and sequential quadratic programming. Bayreuther Math. Schriften 35: 1–37
Alt, W., Kolumbán, I. (1992), An implicit function theorem for a class of monotone generalized equations. Proc of Workshop on Nondifferentiable Problems in Optimal Design. Prague
Alt, W., Kolumbán, I. (to appear), An implicit function theorem for a class of monotone mappings
Ito, K, Kunish, K (1989), Sensitivity analysis of solutions to optimization problems in Hilbert spaces with applications to optimal control and estimation. Preprint
Kassay, G., Kolumbán, I. (1989), Implicit function and variational inequalities for monotone mappings. Babes-Bolyai Univ. Preprint 7: 79–92
Kassay, G. (to appear), On nonsmooth parametric optimization
Malanowski, K (to appear), Second order conditions and constraint qualifications, etc. Appl. Math. Optim.
Robinson, S.M. (1980), Strongly regular generalized equations. Math. Oper. Res. 5: 43–62
Robinson, S.M. (1991), An implicit function theorem for a class of nonsmooth functions. Meth. Oper. Res. 16: 292–309
Rockafellar, R.T. (1976), Monotone operators and the proximal point algorithm. SIAM, J., Control and Optimiz. 14: 877–898
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© 1993 Springer-Verlag Berlin Heidelberg
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Kassay, G. (1993). On the Implicit Function Theorem and Parametric Optimization. In: Karmann, A., Mosler, K., Schader, M., Uebe, G. (eds) Operations Research ’92. Physica, Heidelberg. https://doi.org/10.1007/978-3-662-12629-5_60
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DOI: https://doi.org/10.1007/978-3-662-12629-5_60
Publisher Name: Physica, Heidelberg
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