Analysis on RMIL conjugate gradient method and its variants under exact line search

• Published in: AIP Conference Proceedings
• Main Author: Idalisa N.; Zullpakkal N.; Rivaie M.; Aini N.; Hajar N.; Khadijah W.; Fadhilah N.H.
• Format: Conference paper
• Language: English
• Published: American Institute of Physics 2024
• Online Access: https://www.scopus.com/inward/record.uri?eid=2-s2.0-85188418658&doi=10.1063%2f5.0192308&partnerID=40&md5=896e94db77c3f7450240f8a0aecb1a5a

A great deal of literature is available as a result of the numerous techniques and strategies that have been developed to enhance Conjugate gradient (CG) methodologies. CG is a well-known methodology among researchers in the optimization area, when applied with a suitable coefficient it becomes very efficient. One of the methods is the Rivaie-Mohd-Ismail-Leong (RMIL) method [1] equipped with sufficient descent and global convergent properties by satisfying an upper bound. Yet, there are a few common problems associated with this RMIL method. Many of these problems are related to numerical performance and efficiency, as well as their theoretical properties. The main issue arise when RMIL coefficient cannot satisfies the upper bound, unless it is non-negative, for global convergence. Thus, modification of RMIL method mostly restricts the CG coefficient to be non-negative and is simplified to satisfies the upper bound. Due to this, the purpose of this study is to give global convergence analysis for the RMIL technique under exact line search, regardless of coefficient sign. The comparison is performed based on the number of iterations (NOI) and Central Processing Unit (CPU) times efficiency metric with some variants of RMIL method. Numerical results for a set consisting of 21 unconstrained optimization test problems with various dimension ranges show that the RMIL method outperforms some existing modified RMIL methods. In conclusion, the negative value of beta coefficient will not affect the performance of RMIL method theoretically and numerically. © 2024 Author(s).