Characterizing the nondominated set by separable functions
We present sufficient and necessary conditions for classes of separable (additive) functions to generate the set of nondominated outcomes in multicriteria optimization problems. The basic technique consists of convexifying the set of outcomes and then to apply the standard characterization of a convex set by a class of linear functions. The conditions include the case when the set of feasible alternatives is convex and the criteria are convex-transformable. We show that the sum of powers and the sum of exponents functions can generate the nondominated set for an arbitrary set of outcomes (under compactness conditions). We also discuss monotonicity, proper nondominance, uniqueness and connectedness of solutions, and weights and tradeoffs with respect to these functions.
scientific article; zbMATH DE number 4023043
scientific article