Abstract
The well-posedness concept introduced in Ref. 1 for global optimization problems with a unique solution is generalized here to problems with many minimizers, under the name of extended well-posedness. It is shown that this new property can be characterized by metric criteria, which parallel to some extent those known about generalized Tikhonov well-posedness.
Similar content being viewed by others
References
Zolezzi, T.,Well-Posedness Criteria in Optimization with Application to the Calculus of Variations, Nonlinear Analysis: Theory, Methods and Applications, Vol. 25, pp. 437–453, 1995.
Zolezzi, T.,Well-Posedness of Optimal Control Problems, Control and Cybernetics, Vol. 23, pp. 289–301, 1994.
Bennati, M. L.,Well-Posedness by Perturbation in Optimization Problems and Metric Characterizations, Rendiconti di Matematica (to appear).
Bennati, M. L.,Local Well-Posedness of Constrained Problems, Optimization (to appear).
Dontchev, A. L., andZolezzi, T.,Well-Posed Optimization Problems, Lecture Notes in Mathematics, Springer, Berlin, Germany, Vol. 1543, 1993.
Zolezzi, T.,Extended Well-Posedness of Optimal Control Problems, Discrete and Continuous Dynamical Systems, Vol. 1, pp. 547–553, 1995.
Kuratowski, C.,Topologie, Vol. 1, Panstwowe Wydawnictwo Naukowa, Warszawa, Poland, 1958.
Furi, M., andVignoli, A.,About Well-Posed Optimization Problems for Functionals in Metric Spaces, Journal of Optimization Theory and Applictions, Vol. 5, pp. 225–229, 1970.
Marcellini, P.,Nonconvex Integrals of the Calculus of Variations, Lecture Notes in Mathematics, Springer, Berlin, Germany, Vol. 1446, pp. 16–57, 1990.
Ekeland, I.,Nonconvex Minimization Problems, Bulletin of the American Mathematical Society, Vol. 1, pp. 443–474, 1979.
Author information
Authors and Affiliations
Additional information
Communicated by F. Giannessi
This work was partially supported by MURST, Fondi 40%, Rome, Italy.
Rights and permissions
About this article
Cite this article
Zolezzi, T. Extended well-posedness of optimization problems. J Optim Theory Appl 91, 257–266 (1996). https://doi.org/10.1007/BF02192292
Issue Date:
DOI: https://doi.org/10.1007/BF02192292