Two methods for solving optimization problems arising in electronic measurements and electrical engineering

TL;DR

This paper introduces two novel global optimization methods for locating the first root of an equation in electronic measurements, utilizing Lipschitz constants, with proven convergence and demonstrated effectiveness through numerical experiments.

Contribution

The paper presents two new global optimization algorithms that leverage Lipschitz constants to find roots or minimize functions, with convergence guarantees and practical validation.

Findings

Both methods successfully find the first root or global minimizers.

Numerical experiments confirm the effectiveness of the methods on real and test problems.

The second method adaptively estimates local Lipschitz constants, improving flexibility.

Abstract

In this paper we introduce a common problem in electronic measurements and electrical engineering: finding the first root from the left of an equation in the presence of some initial conditions. We present examples of electrotechnical devices (analog signal filtering), where it is necessary to solve it. Two new methods for solving this problem, based on global optimization ideas, are introduced. The first uses the exact a priori given global Lipschitz constant for the first derivative. The second method adaptively estimates local Lipschitz constants during the search. Both algorithms either find the first root from the left or determine the global minimizers (in the case when the objective function has no roots). Sufficient conditions for convergence of the new methods to the desired solution are established in both cases. The results of numerical experiments for real problems and a set of test functions are also presented.