A Deterministic Program for Obtaining Optima under Constraints for Any Analytical System

TL;DR

This paper introduces a deterministic, step-by-step program based on a Runge-Kutta method for finding optimal solutions under constraints in analytical systems, aiming for global optima without randomness.

Contribution

It presents a novel deterministic algorithm that avoids random guesses, applicable to a wide range of analytical systems, and provides a practical implementation recipe.

Findings

The program can find optimal solutions with or without constraints.

Evidence suggests the method tends toward global optima.

Application examples demonstrate practical utility.

Abstract

Conceptual framework is laid out of a deterministic program capable of obtaining optimum solutions with or without constraints for any reasonably behaved analytical system. Recipe implementable as a well-behaved Runge-Kutta procedure is given. Determinism means no inspired initial guesses or random number trials. The program follows well-defined steps between well-defined start and end points, to a large extent configuration independent. This program is also conjectured to lead to global optimum solutions based on evidence, short of a proof. Application to realistic problems is given as example.