Procedure of constructing a Pareto set for differentiable criteria functions

A ubiquitous computational procedure for the multicriteria optimization allows one to approximate the Pareto set under different requirements to the vector of particular efficiency criteria and the set of feasible solutions. In the paper, it is assumed that particular efficiency criteria are pseudoconcave in an open neighborhood of a compact convex set of feasible solutions which can be given by differentiable functional constraints. To build specific numerical methods for approximating the Pareto set, a rule for choosing the initial approximation and a rule for moving from the current reference solution to the next one are proposed.