Study of convergence rate and efficiency of two-phase methods for approximating the Edgeworth-Pareto hull

The convergence rate and efficiency of two-phase methods for approximating the Edgeworth-Pareto hull in nonlinear multicriteria optimization problems is studied. 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. It is shown that the convergence rate of two-phase methods is determined by the metric properties of the set of local extrema of criteria convolutions, specifically, by its upper metric dimension. The efficiency of two-phase methods is examined; i.e., they are compared with hypothetical optimal methods of the same class. It is shown that the efficiency of two-phase methods is determined by the ratio of the ɛ-entropy and ɛ-capacity for the set of local extrema of criteria convolutions.