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J. Benoist, “Contractibility of the Efficient Set in Strictly Quasi-Concave Vector Maximization,” Journal of Optimization Theory and Applications, Vol. 110, No. 2, 2001, pp. 325-336. doi:10.1023/A:1017527329601

has been cited by the following article:

• TITLE: Compactness, Contractibility and Fixed Point Properties of the Pareto Sets in Multi-Objective Programming

  AUTHORS: Zdravko Dimitrov Slavov, Christina Slavova Evans

  KEYWORDS: Multi-Objective Programming, Pareto-Optimal, Pareto-Front, Compact, Contractible, Fixed Point, Retraction

  JOURNAL NAME: Applied Mathematics, Vol.2 No.5, May 6, 2011

  ABSTRACT: This paper presents the Pareto solutions in continuous multi-objective mathematical programming. We discuss the role of some assumptions on the objective functions and feasible domain, the relationship between them, and compactness, contractibility and fixed point properties of the Pareto sets. The authors have tried to remove the concavity assumptions on the objective functions which are usually used in multi-objective maximization problems. The results are based on constructing a retraction from the feasible domain onto the Pareto-optimal set.