The Detachment Principle and Optimization Methods

Abstract

In Chapter 1, it was shown that in a conservative fi field of forces the problem of equilibrium of a mechanical system, subject to bilateral and unilateral ideal constraints, is mathematically equivalent to the general problem of mathematical progrmaming. And conversely, the problem of constrained maximum or minimum may be interpreted as an equilibrium problem of a mechanical system in a force field determined by an objective function where the given conditions in terms of equations and inequalities may be as analytical expressions for bilateral or unilateral constraints imposed on the system. It is understandable, then, that at the foundation of the theory of extremal problems there must lie the same fundamental principles that are at the foundation of analytical mechanics namely, the principle of virtual displacement and the principle of detachment.

“Physics provides us not only with a reason to solve problems but also helps us in finding means for doing so. This happens in two ways. First, it gives us a presentiment about the solution, and, second, hints at the possible path of arguments.”

Henri Poincare

H. Poincare, Importance of Science.