Modifikasi Stepsize pada Metode Steepest Descent dalam Pengoptimuman Fungsi: Kasus Fungsi Kuadratik Diagonal

Abstract

The steepest descent is one of the methods for unconstrained optimization. This method uses stepsize which is obtained by using exact line searches. The exact line searches along steepest descent direction may found the optimum point slowly. A number of researches have been conducted for solving this weakness by changing the stepsize. Some new stepsizes were developed by Ya-xiang Yuan, Barzilai, and Borwein. In this paper, the execution times and the number of iterations of the steepest descent method, the Ya-xiang Yuan method, and the Barzilai-Borwein method will be compared in solving an unconstrained optimization for diagonal quadratic function case. Numerical results showed that the Ya-xiang Yuan method can find the optimum point within three iterations for two variables functions. Furthermore, the Ya-xiang Yuan method is the most efficient for small scale problems, while the Barzilai-Borwein method showed better results for large scale problems.