Optimization and Suboptimization: The Method of Extended Models in the Non-Linear Case

Abstract

Let us consider some particular optimization problem. Most of ita data is determined by the economic “ environment ”. However, this environment is evolutive, and may be the subject of an optimization research. The particular problem first considered then appears to be a suboptimization , and its results will be valid only if it is separable from its environment. This point of view can be expressed in mathematical terms by considering a “principal” programming problem from which one tries to separate a “reduced” subproblem. The concept of “separability” is defined and studied in the first part of this paper. In the second part, it is used to justify the “Method of Extended Models” as a tool for building optimization models.