Doctorial thesis by ” Aynur Jawdat Namik ” Department of Mathematics<\/p>\n
<\/p>\n
Discussion of the Doctorial thesis in the College of Computer Science and Mathematics -Department of (Department of Mathematics) entitled:<\/p>\n
\u201cInvestigation A New Techniques In Nonlinear Programming With Application\u201d<\/p>\n
<\/p>\n
supervised by Prof. Dr. Eman Tarik Hamed<\/p>\n
<\/p>\n
The thesis addressed.<\/p>\n
This dissertation aims to develop the conjugate gradient method, which is considered one of the most prominent numerical optimization methods for solving unconstrained nonlinear optimization problems, particularly those involving large-scale dimensions. Its widespread use is attributed to its high computational efficiency, fast convergence, low memory requirements, and ease of implementation, making it one of the most reliable and widely adopted methods in scientific and engineering applications.<\/p>\n
This thesis addresses the development and improvement of numerical optimization algorithms, particularly conjugate gradient algorithms and some nature-inspired algorithms such as the spotted hyena pack. The focus is on constructing new coupling parameters and deriving improved search directions based on additional information from function and gradient values, with the aim of increasing convergence efficiency and improving solution quality.<\/p>\n
In the theoretical chapters, Taylor extensions of different orders were used to derive new mathematical relationships, introducing control conditions and coefficients, and combination coefficients. This led to the development of new formulations for coupling parameters and search directions. Some results were also converted to a quasi-Newtonian formula to ensure numerical stability and to prove properties such as positive definition.<\/p>\n
In the applied aspect, a set of different test functions was used to evaluate the performance of the proposed algorithms and compare them with traditional methods using performance metrics such as the number of iterations, the number of evaluations, and convergence speed, in addition to comparison graphs. In the hyena pack algorithm, the group’s coexistence behavior was inspired to develop an efficient search method that balances exploration and exploitation to reach the optimal solution.<\/p>\n
Overall, the thesis concluded that the proposed methods achieve improved numerical performance in terms of convergence speed and solution accuracy compared to traditional methods, while maintaining algorithm stability and applicability to complex nonlinear optimization problems.<\/p>\n
Finally, conclusions based on numerical and statistical comparisons were included, along with recommendations for future work.<\/p>\n
<\/p>\n
The discussion committee consists of<\/p>\n
Dr. Abbas Hassan Taqi (Chairman)<\/p>\n
Dr. Ban Ahmed Hassan (Member)<\/p>\n
Dr. Omar Saber Qassem (Member)<\/p>\n
Dr. Mona Mohsen Mohamed Ali (Member)<\/p>\n
Dr. Hisham Mohammed Khudair (Member)<\/p>\n
Dr. Eman Tarik Hamed (Mem<\/p>\n
ber & Supervisor)<\/p>\n
<\/p>\n","protected":false},"excerpt":{"rendered":"
Doctorial thesis by ” Aynur Jawdat Namik ” Department of Mathematics Discussion of the Doctorial thesis in the College of Computer Science and Mathematics -Department of (Department of Mathematics) entitled: \u201cInvestigation A New Techniques In Nonlinear Programming With Application\u201d supervised by Prof. Dr. Eman Tarik Hamed The thesis addressed. This dissertation aims to develop the conjugate gradient method, which is considered one of the most prominent numerical optimization methods for solving unconstrained nonlinear optimization problems, particularly those involving large-scale dimensions. Its widespread use is attributed to its high computational efficiency, fast convergence, low memory requirements, and ease of [Read More]<\/a><\/p>\n","protected":false},"author":24,"featured_media":43199,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[2],"tags":[],"class_list":["post-43232","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-viva"],"_links":{"self":[{"href":"https:\/\/uomosul.edu.iq\/en\/computerscience\/wp-json\/wp\/v2\/posts\/43232","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/uomosul.edu.iq\/en\/computerscience\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/uomosul.edu.iq\/en\/computerscience\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/uomosul.edu.iq\/en\/computerscience\/wp-json\/wp\/v2\/users\/24"}],"replies":[{"embeddable":true,"href":"https:\/\/uomosul.edu.iq\/en\/computerscience\/wp-json\/wp\/v2\/comments?post=43232"}],"version-history":[{"count":2,"href":"https:\/\/uomosul.edu.iq\/en\/computerscience\/wp-json\/wp\/v2\/posts\/43232\/revisions"}],"predecessor-version":[{"id":43234,"href":"https:\/\/uomosul.edu.iq\/en\/computerscience\/wp-json\/wp\/v2\/posts\/43232\/revisions\/43234"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/uomosul.edu.iq\/en\/computerscience\/wp-json\/wp\/v2\/media\/43199"}],"wp:attachment":[{"href":"https:\/\/uomosul.edu.iq\/en\/computerscience\/wp-json\/wp\/v2\/media?parent=43232"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/uomosul.edu.iq\/en\/computerscience\/wp-json\/wp\/v2\/categories?post=43232"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/uomosul.edu.iq\/en\/computerscience\/wp-json\/wp\/v2\/tags?post=43232"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}