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Contractibility of Efficient Frontier of Simply Shaded Sets

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Abstract

In finite dimensional Euclidean space, we prove the contractibility of the efficient frontier of simply shaded sets. This work extends the result of Peleg [7], which confirms the contractibility of the efficient frontier in the convex case.

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References

  1. Benoist, J. (1998), Connectedness of the efficient set for strictly quasiconcave sets, J. Optim. Theory Appl. 96: 627-654.

    Google Scholar 

  2. Benoist, J. and Popovici N. (2000), The structure of the efficient frontier of finite dimensional completely-shaded sets, J. Math. Anal. Appl. 250: 98-117.

    Google Scholar 

  3. Benoist, J. and Popovici N. (2001), The contractibility of the efficient frontier for three dimensional simply shaded sets, J. Optim. Theory Appl. 111: 81-116.

    Google Scholar 

  4. Daniilidis, A., Hadjisavvas, N. and Schaible S. (1997), Connectedness of the efficient set for three-objective quasiconcave maximization problem, J. Optim. Theory Appl. 93: 517-524.

    Google Scholar 

  5. Debreu, G. (1959), Theory of value, John Wiley, New York.

    Google Scholar 

  6. Luc, D.T. (1989), Theory of Vector Optimization, Lecture Notes in Economics and Mathematical Systems, Vol. 319, Springer Verlag, Berlin.

    Google Scholar 

  7. Peleg, B. (1972), Topological properties of the efficient point set, Proc. Amer. Math. Soc. 35: 531-536.

    Google Scholar 

  8. Sun, E.J. (1996), On the connectedness of the efficient set for strictly quasiconvex vector minimization problems, J. Optim. Theory Appl. 89: 475-481.

    Google Scholar 

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Benoist, J. Contractibility of Efficient Frontier of Simply Shaded Sets. Journal of Global Optimization 25, 321–335 (2003). https://doi.org/10.1023/A:1022448811953

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  • DOI: https://doi.org/10.1023/A:1022448811953

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