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

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.