College of Computer Science and Mathematics

Discussion of Ph.D Dissertation  in the College of Computer Science and Mathematics – Department of Mathematics Sciences entitled:

“ Several Important Developments in Memoryless and Preconditioned Conjugate Gradient Algorithms in Unconstrained Optimization “

It was discussed in the discussion room at the Faculty of Computer Science and Mathematics at the University of Mosul on Monday, 17-3-2025

Ph.D. Dissertation by student Sabreen Mahmoud abbas, under the supervision of       6-       Professor Dr. Abbas Younis Elias and  Professor Dr. Maysoun Mal Allah Aziz

This thesis focusses on enhancing and refining various iterative regression methods to address unconstrained optimisation issues, while also increasing the efficacy of these algorithms for problems of varying dimensions.

The first and second chapters included a comprehensive and precise review of the methods and types of conjugate gradient techniques. In the third chapter we introduce a novel class of hybrid nonlinear conjugate gradient algorithms that generate an adequate search direction for descending gradients at each iteration. Functions that are not convex in general, we show that the suggested approaches converge globally under certain conditions. Numerical findings demonstrate the effectiveness of these new and publish  novel hybrid approaches on the specified selected test problems compared with the standard (Maulana CG,2022) algorithms.

In chapter four, we are trying to accelerate the speed of the algorithms developed in the previous chapter, and these algorithms are accelerated by full two-rank VM updates. In the fifth chapter, we imply a novel memoryless CG-methods for the previous optimized CG-algorithms.

chapter six contains a comparison of numerical results and an analysis of these results, while finding critical conclusions in the field of application and providing suggestions for future work.

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The scientific committee included the following members:

• Professor Dr. Abbas Hassan Taqi – Chairman
• Professor Dr. Abbas Khader Abbou – Member.
• Professor Dr. Basem Abbas Hassan – Member.
• Professor Dr. Hoda Essam Ahmed – Member.
• Professor Dr. Hamsa Tharwat Saeed – Member.
• Professor Dr. Abbas Younis Elias- Member and supervisor

7-Professor Dr. Maysoun Mal Allah Aziz – Member and supervisor.