Title: Numerical optimisation technique to solve imprecisely defined nonlinear system of equations with bounded parameters

Authors: Sukanta Nayak; J. Pooja

Addresses: Department of Mathematics, School of Advanced Sciences, VIT-AP University, Amaravati, Andhra Pradesh, India ' Department of Mathematics, Amrita School of Engineering, Amrita Vishwa Vidyapeetham, Coimbatore, India

Abstract: This paper includes an optimisation algorithm to estimate the solution of interval nonlinear system of equations. First, the proposed optimisation algorithm converts interval nonlinear system of equations to unconstrained multivariable optimisation problem with interval uncertainties. Then the interval unconstrained multivariable optimisation problem is investigated by using inner-outer direct search approach. Finally, the obtained solutions are assembled and using the regularity principle, interval solutions are obtained. Considering these steps together, this method is named as inner outer direct search (IODS) algorithm for interval unconstrained multivariable optimisation. Example problems are investigated to demonstrate the IODS algorithm and compared the obtained results with the results by using Krawczyk, vertex and Newton's methods.

Keywords: uncertainty; interval nonlinear system of equations; unconstrained multi-variable optimisation; inner-outer direct search; uncertain width.

DOI: 10.1504/IJMOR.2022.127381

International Journal of Mathematics in Operational Research, 2022 Vol.23 No.3, pp.394 - 411

Received: 30 Mar 2021
Accepted: 10 Jun 2021
Published online: 01 Dec 2022 *

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