| Biography | |
|---|---|
 Prof. Saman Babaie-Kafaki Semnan University, Iran |
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| Title: Modified conjugate gradient methods based on singular value analysis | |
| Abstract: Optimization, as a topic of great significance in nonlinear analysis and optimal control, is widely and increasingly used in engineering, economics, management, industry, and other areas. Among the efficient continuous optimization algorithms, conjugate gradient (CG) methods have attracted special attentions because of low-memory requirement, simplicity of the implementation, implicit usage of second-order information and desirable convergence. The methods have been widely employed by engineers and mathematicians engaged in solving large-scale problems which frequently appear in many real world disciplines such as image restoration, compressed sensing, nonnegative matrix factorization, neural network training and so on. Here, CG methods are studied in a matrix point of view in the sense of conducting singular value analysis on the search direction matrix. Especially, the open problem of finding optimal value for parameter of the well-known Dai-Liao CG method is discussed. It is also described that how a search direction near to the direction of the maximum magnification by search direction matrix of the Dai-Liao method can affect performance of the method. Numerical effects of the corresponding achievements are concisely presented as well. Finally, some possible future studies are stated. | |
| Biography: Saman Babaie–Kafaki is a Professor in Department of Mathematics of Semnan University, Iran. He received his B.Sc. in Applied Mathematics from Mazandaran University, Iran, in 2003, and his M.Sc. and Ph.D. in Applied Mathematics from Sharif University of Technology, Iran, in 2005 and 2010, respectively, under supervision of Professor Nezam Mahdavi–Amiri. His research interests lie within numerical optimization, matrix computations, image/signal processing, linear regression and heuristic algorithms. | |
