Abstract
In this paper, the concept of extended well-posedness of scalar optimization problems introduced by Zolezzi is generalized to vector optimization problems in three ways: weakly extended well-posedness, extended well-posedness, and strongly extended well-posedness. Criteria and characterizations of the three types of extended well-posedness are established, generalizing most of the results obtained by Zolezzi for scalar optimization problems. Finally, a stronger vector variational principle and Palais-Smale type conditions are used to derive sufficient conditions for the three types of extended well-posedness.
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References
Dentchev, A. L., and Zolezzi, T., Well-Posed Optimization Problems, Lecture Notes in Mathematics, Springer Verlag, Berlin, Germany, Vol. 1543, 1993.
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., Extended Well-Posedness of Optimization Problems, Journal of Optimization Theory and Applications, Vol. 91, pp. 257-266, 1996.
Bednarczuk, E., Well-Posedness of Vector Optimization Problems, Lecture Notes in Economics and Mathematical Systems, Springer Verlag, Berlin, Germany, Vol. 294, pp. 51-61, 1987.
Lucchetti, R., Well-Posedness toward Vector Optimization, Lecture Notes in Economics and Mathematical Systems, Springer Verlag, Berlin, Germany, Vol. 294, pp. 194-207, 1987.
Loridan, P., Well-Posed Vector Optimization, Recent Developments in Well-Posed Variational Problems, Mathematics and Its Applications, Kluwer Academic Publishers, Dordrecht, Holland, Vol. 331, pp. 171-192, 1995.
Dencheva, D., and Helbig, S., On Variational Principles, Level Sets, Well-Posedness, and ∈-Solutions in Vector Optimization, Journal of Optimization Theory and Applications, Vol. 89, pp. 329-349, 1996.
Tammer, C., A Generalization of Ekeland's Variational Principle, Optimization, Vol. 25, pp. 129-141, 1992.
Aubin, J. P., and Ekeland, I., Applied Nonlinear Analysis, John Wiley, New York, NY, 1984.
Kuratowski, C., Topologie, Vol. 1, Panstwowe Wydawnicto Naukowa, Warszawa, Poland, 1958.
Chen, G. Y., and Huang, X. X., A Unified Approach to the Existing Three Types of Variational Principles for Vector-Valued Functions, Mathematical Methods of Operations Research, Vol. 48, 1998.
Sawaragi, Y., Nakayama, X. X., and Tanino, T., Theory of Multiobjective Optimization, Academic Press, New York, NY, 1985.
Luc, D. T., Theory of Vector Optimization, Springer, Berlin, Germany, 1989.
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Huang, X.X. Extended Well-Posedness Properties of Vector Optimization Problems. Journal of Optimization Theory and Applications 106, 165–182 (2000). https://doi.org/10.1023/A:1004615325743
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DOI: https://doi.org/10.1023/A:1004615325743