Robinson's implicit function theorem

• Autorzy: Dontchev A. L.
• Języki publikacji: EN

Abstrakty

EN

Robinson's implicit function theorem has played a mayor role in the analysis of stability of optimization problems in the last two decades. In this paper we take a new look at this theorem, and with an updated terminology go back to the roots and present some extensions.

Słowa kluczowe

EN

implicit function; sensitivity; variational inequality; optimization

PL

funkcja uwikłana; czułość; nierówność wariacyjna; optymalizacja

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2003
• Tom: Vol. 32, no 3
• Strony: 529--541
• Opis fizyczny: Bibliogr. 9 poz.

Twórcy

autor

Dontchev A. L.

Bibliografia

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• Levy A.B. (2000) Calm minima in parameterized finite-dimensional optimization, SIAM J. Optim. 11, 160–178.
• Malanowski, K. (2001a) Stability and sensitivity analysis for optimal control problems with control-state constraints. Dissertationes Math. 394.
• Malanowski, K. (2001b)Bouligand differentiability of solutions to parametric optimal control problems. Numer. Funct. Anal. Optim. 22, 973–990.
• Robinson, S.M. (1980) Strongly regular generalized equations, Math. of Oper. Research 5, 43–62.
• Robinson, S.M. (1991) An implicit-function theorem for a class of nonsmooth functions. Math. of Oper. Research 16, 292–309.
• Wets, R.J.-B. and Rockafellar, R.T. (1997) Variational Analysis, Springer-Verlag, Berlin