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

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.

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.

Keywords

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

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

Cite this paper

nullZ. Slavov and C. Evans, "Compactness, Contractibility and Fixed Point Properties of the Pareto Sets in Multi-Objective Programming,"*Applied Mathematics*, Vol. 2 No. 5, 2011, pp. 556-561. doi: 10.4236/am.2011.25073.

nullZ. Slavov and C. Evans, "Compactness, Contractibility and Fixed Point Properties of the Pareto Sets in Multi-Objective Programming,"

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