The reduction of the problem of maximization of the fraction of two functionals

TL;DR

This paper introduces an algorithm that simplifies the problem of maximizing the ratio of two functionals by transforming it into a more manageable form involving maximization of their difference and solving a scalar equation.

Contribution

The paper presents a novel algorithm that reduces the fractional maximization problem to a difference maximization and scalar equation solution, enhancing problem-solving efficiency.

Findings

Algorithm successfully reduces fractional maximization to simpler steps.

Applied to example problems, demonstrating effectiveness.

Provides a new approach for fractional functional optimization.

Abstract

We propose an algorithm for reduction of the problem of maximization of fraction of two functionals to the equivalent procedure including maximization of difference between the functionals and the solution of an equation of scalar unknown. For illustration of the algorithm we solve some problems of the described type.