Discussion of the Doctorial thesis in the College of Computer Science and Mathematics -Department of (Department of Mathematics) entitled:

The Accelerated Conjugate Gradient Method with New Parameters for Unconstrained Optimization Problems

supervised by  Prof. Dr. Ghada Moayid Rasheed AL-Naemi

The thesis addressed.

This thesis aims to develop novel parameters in the field of numerical

optimization, focusing on gradient algorithms, to improve the theoretical

efficiency and numerical performance of unconstrained optimization problems,

particularly large-scale problems. A set of proposed parameters was derived

using various formulas, including the low-memory BFGS method, 𝜂𝑛−1

derivation, spectral parameters, and binomial conjugate gradient algorithms.

These parameters underwent rigorous mathematical analysis, and their

fundamental properties, including adequate regression and overall convergence,

were proven under appropriate standard assumptions.

To assess the efficiency of the proposed parameters, comprehensive

numerical experiments were conducted using 46 standard test functions,

compared with two commonly used classical parameters, and systematic

comparisons were made with established traditional methods. The results

showed a significant advantage for the proposed parameters in terms of

convergence speed and numerical stability.

The discussion committee consists of

• Dr. Ali Hassan Nasser Al-Fayadh (Chairman)
• Dr. Basim Abbas Hassan (Member)
• Dr. Hamsa Tharwat Saeed (Member)
• Dr. Abdul-Ghafoor Mohammed Ameen Khidr (Member)
• Dr. Hisham Mohammed Khidr (Member)
• Dr. Ghada Muayyad Rasheed (Member & Supervisor)