An Efficient Hybrid Conjugate Gradient Method for Unconstrained Optimisation

Mamat, Prof. Dr. Mustafa (2020) An Efficient Hybrid Conjugate Gradient Method for Unconstrained Optimisation. In: Forum for Interdisciplinary Mathematics. Springer, pp. 191-207. ISBN 23646748

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Abstract

Optimisation refers to a common procedure applied within the science and engineering domain to determine variables that produce the best performance values. One of the common efficient techniques to solve large-scale unconstrained optimisation issues is the conjugate gradient method, because of its simplicity, low memory consumptions and global convergence properties. This method embeds the n-step to attain a minimum point, where convergence properties are absent. Several techniques do not perform well according to the number of iteration and CPU time. In order to address these shortcomings, this study proposed new Hybrid CG coefficients, β , Tal’at and Mamat (HTM). The proposed parameter βkHTM is computed as a combination of βkHS (Hestenes–Steifel formula), βkLS (Liu–Storey formula) and βkRMIL (Rivaie formula) to exploit attractive features of each. The algorithm uses the exact line search. Numerical results and their performance profiles display that the proposed method is promising. It is also shown that’s the new formula for β performs much better than the original Hestenes–Steifel, Liu–Storey and the Rivaie methods. © 2020, The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

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