Title: Conjugate gradient with Armijo line search approach to investigate imprecisely defined unconstrained optimisation problem

Authors: Paresh Kumar Panigrahi; Sukanta Nayak

Addresses: Department of Mathematics, School of Advanced Sciences, VIT-AP University, Inavolu, Beside AP Secretariat, Amaravati, AP, India ' Department of Mathematics, School of Advanced Sciences, VIT-AP University, Inavolu, Beside AP Secretariat, Amaravati, AP, India

Abstract: The main focus of the study is to investigate nonlinear systems with uncertainties. Here the epistemic type of uncertainties is considered as fuzzy. As such, the present study analyses fuzzy nonlinear systems. In order to solve the fuzzy nonlinear systems, one of the ways is to transform the system into a fuzzy unconstrained optimisation problem. In this context, the concept of conjugate gradient descent optimisation method is used with fuzziness, and the fuzzy parameters are used to develop the fuzzy conjugate gradient descent optimisation (FCGDO) algorithm to solve the fuzzy unconstrainted nonlinear optimisation problem. The significance of the FCGDO algorithm is used to fuzzy parameter the Armijo-type line search perform to guarantee that it possesses fast convergence for large-scale problems. Then, the convergence study and comparison are done with seven other approaches with the same case studies and it is found that the proposed algorithm performs well. Further, to quantify the uncertainties, the system is investigated with fuzzy and fully fuzzy through the case study. The impact of this algorithm is expected to handle various real-life application problems where uncertainty exists, and this advancement and improvement can be implemented in future directions of research in both academia and industry.

Keywords: fuzzy set; triangular fuzzy number; TFN; unconstrained optimisation problem; fuzzy conjugate gradient descent optimisation technique; FCGDO; convergence analysis.

DOI: 10.1504/IJCSE.2024.139711

International Journal of Computational Science and Engineering, 2024 Vol.27 No.4, pp.458 - 471

Received: 02 Jun 2023
Accepted: 07 Aug 2023
Published online: 05 Jul 2024 *

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