Convergence analysis of two-phase methods for approximating the Edgeworth-Pareto hull in nonlinear multicriteria optimization problems

The convergence of two-phase methods for approximating the Edgeworth-Pareto hull (EPH) in nonlinear multicriteria optimization problems is analyzed. The methods are based on the iterative supplement of the finite set of feasible criteria vectors (approximation basis) whose EPH approximates the desired set. A feature of two-phase methods is that the criteria images of randomly generated points of the decision space approach the Pareto frontier via local optimization of adaptively chosen convolutions of criteria. The convergence of two-phase methods is proved for both an abstract form of the algorithm and for a two-phase method based on the Germeier convolution.