Approximation of Multi-Dimensional Edgeworth-Pareto Hull in Non-linear Multi-Objective Problems

摘要

The paper is devoted to approximating the multi-dimensional Edgeworth-Pareto Hull, which is a tool for decision support in multi-objective optimization problems. The notion of the Edgeworth-Pareto Hull is introduced. It is demonstrated how the effective hull of a non-convex multi-dimensional set given by a mapping can be approximated by the product (intersection) of a finite number of Edgeworth-Pareto Hulls. Then, a new numerical technique for approximating the non-convex EPH for complicated problems is proposed and its properties are discussed.