On the Implicit Function Theorem and Parametric Optimization

  • G. Kassay
Conference paper


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)).


  1. Alt, W. (1990), The Lagrange-Newton method for infinite-dimensional optimization problems. Numer Funct Anal and Optimiz 11: 201–224CrossRefGoogle Scholar
  2. Alt, W. (1991), Parametric programming with application to optimal control and sequential quadratic programming. Bayreuther Math. Schriften 35: 1–37Google Scholar
  3. 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. PragueGoogle Scholar
  4. Alt, W., Kolumbán, I. (to appear), An implicit function theorem for a class of monotone mappingsGoogle Scholar
  5. Ito, K, Kunish, K (1989), Sensitivity analysis of solutions to optimization problems in Hilbert spaces with applications to optimal control and estimation. PreprintGoogle Scholar
  6. Kassay, G., Kolumbán, I. (1989), Implicit function and variational inequalities for monotone mappings. Babes-Bolyai Univ. Preprint 7: 79–92Google Scholar
  7. Kassay, G. (to appear), On nonsmooth parametric optimization Google Scholar
  8. Malanowski, K (to appear), Second order conditions and constraint qualifications, etc. Appl. Math. Optim.Google Scholar
  9. Robinson, S.M. (1980), Strongly regular generalized equations. Math. Oper. Res. 5: 43–62CrossRefGoogle Scholar
  10. Robinson, S.M. (1991), An implicit function theorem for a class of nonsmooth functions. Meth. Oper. Res. 16: 292–309CrossRefGoogle Scholar
  11. Rockafellar, R.T. (1976), Monotone operators and the proximal point algorithm. SIAM, J., Control and Optimiz. 14: 877–898CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • G. Kassay
    • 1
  1. 1.Faculty of MathematicsBabes-Bolyai University ClujClujRomania

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