Abstract
In this paper we give a detailed proof for a theorem due to D. T. Luc saying that the efficient and weakly efficient sets of compact convex subsets of R 2 are homeomorphic to certain simplexes. An example is designed to analyze the proof scheme of Luc for this theorem.
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References
D.T. Luc, Structure of the efficient point sets, Proc. Amer. Math. Soc. Vol. 95, 1985, 433–440.
D.T. Luc, Theory of Vector Optimization, Lecture Notes in Economics Mathematical Systems, Vol. 319, Springer-Verlag, Berlin, 1989.
D.T. Luc, Contractibility of efficient sets in normed space, Nonlinear Anal. Theory Methods & Appl. Vol. 15, 1990, 527–535.
B. Peleg, Topological properties of the efficient point set, Proc. Amer. Math. Soc. Vol. 35, 1972, 531–536.
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© 2003 Kluwer Academic Publishers
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Huy, N.Q., Phuong, T.D., Yen, N.D. (2003). On the Contractibility of the Efficient and Weakly Efficient Sets in R 2 . In: Daniele, P., Giannessi, F., Maugeri, A. (eds) Equilibrium Problems and Variational Models. Nonconvex Optimization and Its Applications, vol 68. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0239-1_13
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DOI: https://doi.org/10.1007/978-1-4613-0239-1_13
Publisher Name: Springer, Boston, MA
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