Min-max formulation of the balance number in multiobjective global optimization

The notion of the balance number introduced by Galperin through a certain set contraction procedure for nonscalarized multiobjective global optimization is represented via a min-max operation on the data of the problem. This representation yields a different computational procedure for the calculation of the balance number and allows us to generalize the approach for problems with countably many performance criteria. Comparisons with Pareto optimality and compromise solutions are discussed and illustrated by examples. It is demonstrated that lp-norm scalarizations (1 ≤ p < ∞), cf., [1–3], do not cover the entire Pareto set.