The applications of fixed-point theorem in optimisation problems

Abstract

Abstract:The fixed-point theorem is widely used in different engineering applications. The present paper focuses on its applications in optimisation. A Matlab toolbox, which implements the branch-and-bound optimisation method based on the fixed-point theorem, is used for solving different real-life test problems, including estimation of model parameters for the Jiles-Atherton model.

Using a Jiles‐Atherton vector hysteresis model for isotropic magnetic materials with the finite element method, Newton‐Raphson method, and relaxation procedure

“…The coils have 220 turns in both test cases. The JA model coefficients used correspond to nonoriented M330‐50 A steel sheet: m s = 1.28 × 10 6 A/m, a = 26.1 A/m, k = 52.3 A/m, c = 0.13, and α j = 7.45 × 10 −5 . A 1 second time interval, ie, 50 periods, have been simulated, with 200 time steps per period by default.…”

“…Note that the identification of the hysteresis models is widely discussed in the literature, eg, in Chwastek and Zaman and Matin for JA parameters or in Zaman and Sikder for identification of the Bouc‐Wen hysteresis model. The methods for the identification of the JA parameters are not discussed in the following of this paper.…”

Existence of common fixed points for linear combinations of contractive maps in enhanced probabilistic metric spaces

“…In recent times, fixed point theory has become an important tool in pure and applied sciences, such as biology [4], chemistry [25], economics [10], engineering and physics, to cite just a few. The Banach's fixed point theory, widely known as the contraction principle, is an important tool in the theory of metric spaces [14,22].…”