Hostname: page-component-848d4c4894-p2v8j Total loading time: 0.001 Render date: 2024-05-19T12:31:24.719Z Has data issue: false hasContentIssue false
  • English
  • Français

About a local approximation theorem and an inverse function theorem

Published online by Cambridge University Press:  17 February 2009

J. W. Nieuwenhuis
J. W. Nieuwenhuis
Affiliation:
Econometric Institute University of Groningen, P. O. Box 800, 9700 AV Groningen, The Netherlands
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

This paper gives a theorem by which it is possible to derive in an easy way a local approximation theorem and an inverse function theorem. The latter theorems are not new. The main advantage of our paper is in giving a relatively short route to these results.

Type
Research Article
Information
The ANZIAM Journal , Volume 22 , Issue 2 , October 1980 , pp. 185 - 192
Copyright
Copyright © Australian Mathematical Society 1980

References

[1]Craven, B. D., “A generalization of Lagrange multipliers”, Bull. Austral. Math. Soc. 3 (1970), 353–362.CrossRefGoogle Scholar
[2]Craven, B. D., Mathematical programming and control theory (Chapman and Hall, London, 1978).CrossRefGoogle Scholar
[3]Liusternik, L. and Sobolev, V., Elements of functional analysis (Frederick Ungar, New York, 1961).Google Scholar
[4]Luenberger, D. G., Optimization by vector space methods (Wiley, 1969).Google Scholar
[5]Robinson, S. M., “Normed convex processes”, Trans. Amer. Math. Soc. 174 (1972), 127–140.CrossRefGoogle Scholar
[6]Robinson, S. M., “An inverse function theorem for a class of multivalued functions”, Proc. Amer. Math. Soc. 41 (1973), 211–218.CrossRefGoogle Scholar
[7]Robinson, S. M., “Stability theory for systems of inequalities, Part II: Differentiable nonlinear systems”, SIAM J. Num. Anal 13 (1976), 497–513.CrossRefGoogle Scholar
[8]Rockafellar, R. T., Convex analysis (Princeton University Press, Princeton, New Jersey, 1970).CrossRefGoogle Scholar
[9]Tuy, H., “On the convex approximation of nonlinear inequalities”, Math. Operationsforsch. u. Statist. 5 (1974), 451–464.CrossRefGoogle Scholar