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Characterizations of the Nonemptiness and Compactness of Solution Sets in Convex Vector Optimization

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Abstract

In this paper, various necessary and sufficient conditions are given for the nonemptiness and compactness of the weakly efficient solution set of a convex vector optimization problem.

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References

  1. Chen, G. Y., and Craven, B. D., Existence and Continuity of Solutions for Vector Optimization, Journal of Optimization Theory and Applications, Vol. 81, pp. 459–467, 1994.

    Google Scholar 

  2. Sawaragi, Y., Nakayama, H., and Tanino, T., Theory of Multiobjective Optimization, Academic Press, New York, New York, 1985.

    Google Scholar 

  3. Borwein, J. M., On the Existence of Pareto Efficient Points, Mathematics of Operations Research, Vol. 8, pp. 64–73, 1983.

    Google Scholar 

  4. Henig, M. I., Existence and Characterization of Efficient Decisions with Respect to Cones, Mathematical Programming, Vol. 23, pp. 111–116, 1982.

    Google Scholar 

  5. Bitran, G. R., and Magnanti, T. L., The Structure of Admissible Points with Respect to Cone Dominance, Journal of Optimization Theory and Applications, Vol. 29, pp. 573–614, 1979.

    Google Scholar 

  6. Rockafellar, R. T., and Wets, R. J. B., Variational Analysis, Springer Verlag, Berlin, Germany (to appear).

  7. Rockafellar, R. T., Convex Analysis, Princeton University Press, Princeton, New Jersey, 1970.

    Google Scholar 

  8. Deng, S., On Approximate Solutions in Convex Vector Optimization, SIAM Journal on Control and Optimization, Vol. 35, pp. 2128–2136, 1997.

    Google Scholar 

  9. Hiriart-Urruty, J. B., and Lemarechal, C., Convex Analysis and Minimization Algorithms, Springer Verlag, Berlin, Germany, 1993.

    Google Scholar 

  10. Ruiz-Canales, P., and Rufian-Lizana, A., A Characterization of Weakly Efficient Points, Mathematical Programming, Vol. 68, pp. 205–212, 1995.

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematical Sciences, Northern Illinois University, DeKalb, Illinois

    S. Deng (Assistant Professor)

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  1. S. Deng
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Deng, S. Characterizations of the Nonemptiness and Compactness of Solution Sets in Convex Vector Optimization. Journal of Optimization Theory and Applications 96, 123–131 (1998). https://doi.org/10.1023/A:1022615217553

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  • DOI: https://doi.org/10.1023/A:1022615217553

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