Infinite dimensional optimistic optimisation with applications on physical systems

TL;DR

This paper introduces a new numerical optimization method for infinite dimensional problems that requires minimal assumptions, demonstrating superior convergence and accuracy on physical system applications like brachistochrone and catenary problems.

Contribution

The paper proposes a novel infinite dimensional optimization algorithm that does not rely on derivative information and outperforms existing methods in convergence speed and solution accuracy.

Findings

Achieves solutions close to true optima within 1000 evaluations

Demonstrates better convergence than existing algorithms on physical problems

Effective for complex infinite dimensional functional optimization

Abstract

This paper presents a novel numerical optimisation method for infinite dimensional optimisation. The functional optimisation makes minimal assumptions about the functional and without any specific knowledge on the derivative of the functional. The algorithm has been tested on several physical systems (brachistochrone and catenary problems) and it is shown that the solutions obtained are close to the actual solutions in one thousand functional evaluations. It is also shown that for the tested cases, the new algorithm provides better convergence to the optimum value compared to the tested existing algorithms.