Abstract
A new method for solving Large-Scale problems in the unconstrained optimization has been proposed in this research depending on the BFGS method. The limited memory is used in the BFGS method by multiplying the BFGS matrix by a vector to obtain vectors instead of matrices and only two vectors can be stored, by modifying the algorithm given by Nocedal J (1999). The purpose of this algorithm is to enable us to solving the Large-Scale Problems, as it is obvious to everyone that the computer can store millions of vectors, whereas its ability in storing matrices is limited. The present method in this research is applied on seven nonlinear functions in order to evaluate the method efficiency in the numbers of iterations (NOI), number of functions (NOF) and function value and comparing it with the standard BFGS method after updating. This method has been applied on functions with variables till 1000000 and more than that. From comparing the results, we fined that this algorithm was the best.
Highlights
E BFGS matrix by a vector to obtain vectors instead of matrices and only two vectors can be stored, by modifying the algorithm given by Nocedal J (1999)
The present method in this research is applied on seven nonlinear functions in order to evaluate the method efficiency in the numbers of iterations (NOI), number of functions (NOF) and function value and comparing it with the standard BFGS method after updating
وم النتاا الإجمالية لملذل الداللة تبلي صح هنلا حئلبة تحئلي بلدرها (95.0) %بالنئلبة إلى numbers of iterations (NOI)مع حئبة تحئي بدرها (93.9) %بالنئبة إلى
Summary
E BFGS matrix by a vector to obtain vectors instead of matrices and only two vectors can be stored, by modifying the algorithm given by Nocedal J (1999). Gk Hessianالتي تقر يوساطة الم ل وفة المتنلاةرة الموجبلة التعريل ، H kوالتلي ت لحم مل ت ارر إلى ت ارر. H k+1 = H k + k حيث kهي الم وفة الم ححة الموجبة التعري وصحما تحقط شرط ،QNوهو:
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