×

Extended well-posedness of optimization problems. (English) Zbl 0873.90094

Summary: The well-posedness concept introduced previously by the author [Nonlinear Anal., Theory Methods Appl. 25, No. 5, 437-453 (1995; Zbl 0841.49005)] 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.

MSC:

90C30 Nonlinear programming

Citations:

Zbl 0841.49005
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] 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. · Zbl 0841.49005 · doi:10.1016/0362-546X(94)00142-5
[2] Zolezzi, T.,Well-Posedness of Optimal Control Problems, Control and Cybernetics, Vol. 23, pp. 289–301, 1994. · Zbl 0810.49010
[3] Bennati, M. L.,Well-Posedness by Perturbation in Optimization Problems and Metric Characterizations, Rendiconti di Matematica (to appear). · Zbl 0885.49017
[4] Bennati, M. L.,Local Well-Posedness of Constrained Problems, Optimization (to appear). · Zbl 0867.49020
[5] Dontchev, A. L., andZolezzi, T.,Well-Posed Optimization Problems, Lecture Notes in Mathematics, Springer, Berlin, Germany, Vol. 1543, 1993. · Zbl 0797.49001
[6] Zolezzi, T.,Extended Well-Posedness of Optimal Control Problems, Discrete and Continuous Dynamical Systems, Vol. 1, pp. 547–553, 1995. · Zbl 0867.49021 · doi:10.3934/dcds.1995.1.547
[7] Kuratowski, C.,Topologie, Vol. 1, Panstwowe Wydawnictwo Naukowa, Warszawa, Poland, 1958.
[8] 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. · Zbl 0188.48802 · doi:10.1007/BF00927717
[9] Marcellini, P.,Nonconvex Integrals of the Calculus of Variations, Lecture Notes in Mathematics, Springer, Berlin, Germany, Vol. 1446, pp. 16–57, 1990. · Zbl 0735.49002
[10] Ekeland, I.,Nonconvex Minimization Problems, Bulletin of the American Mathematical Society, Vol. 1, pp. 443–474, 1979. · Zbl 0441.49011 · doi:10.1090/S0273-0979-1979-14595-6
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.