Application of the $\Lambda$–monotonicity to the search for optimal solutions in higher-dimensional problems

The notion of Pareto optimality is widely used for solving many practical problems. The notion of $\Lambda$-optimality is a generalization of the Pareto optimality; the set of $\Lambda$-optimal solutions can be either wider or narrower than the set of Pareto-optimal solutions. In this paper, we generalize some results for $\Lambda$-optimal target functions obtained earlier, introduce the notion of a critical set of $\Lambda$-optimal solutions, and discuss certain approaches to construction of optimal solutions.