Balance set and Pareto solutions in linear space with application to ongoing optimal resource allocation, investment planning, production, and control problems with multiple objectives

Abstract

The notion of balance set is extended onto infinite-dimensional linear spaces. For multiobjective problems of ongoing optima, resource allocation, continuing investment planning with risk forecasting, optimal production models with time-varying objectives, the notion of finite causality is introduced leading to separable programs and sequential (not necessarily convergent) balance and Pareto sets. Selector sequences (or functions for continuous models) are proposed to determine particular Pareto solutions obtained from infinite sequences of the balance set equations. The method is extended onto multicriteria, global optimal control problems, and the use of Schauder bases is made for obtaining monotonic approximations to the sets of balance points and Pareto solutions. An algorithm is tien proposed for computing those approximations and illustrated by a practical example of the bicriteria min-time, min-fuel vertical soft landing problem to facilitate software design.