The Fixed Point Property in Convex Multi-objective Optimization Problem
نویسنده
چکیده
In this paper we study the Pareto-optimal solutions in convex multi-objective optimization with compact and convex feasible domain. One of the most important problems in multi-objective optimization is the investigation of the topological structure of the Pareto sets. We present the problem of construction of a retraction function of the feasible domain onto Paretooptimal set, if the objective functions are concave and one of them is strictly quasi-concave on compact and convex feasible domain. Using this result it is also proved that the Pareto-optimal and Pareto-front sets are homeomorphic and they have the fixed point property. 2000 Mathematics Subject Classification: 90C29
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