Multiobjective Inverse Problems with Ecological and Economical Motivations

Summary

The paper is devoted to some problems of multiobjective analysis which can be briefly outlined as follows. Two groups of restrictions on a variable x are given. The first one is treated as preassigned constraints and depends on the vector parameter v, while the second group corresponds to controllable restrictions depending on the vector parameter μ. The following reciprocal problems are studied: find the set of controllable parameters m (the inputs of the system) which ensure the preassigned constraints on the variable x with n being given, and vice versa, specify the set of guaranteed values v (the outputs) for the fixed p. The paper deals with the structure, description and “extremal” elements of the above sets. Computerized implementation is also discussed. The questions under consideration are motivated by ecological and economical problems and closely related to those investigated in Kurzhanski (1986), Konstantinov (1983), Nikonov (1988), (1992).