Steepest descent method implementation on unconstrained optimization problem using C++ program

Indonesian Operations Research Association - International Conference on Operations Research 2017

Napitupulu, H.^1 ; Sukono^1 ; Mohd, I Bin^2 ; Hidayat, Y.^3 ; Supian, S.^1

Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran, Indonesia^1

Institute for Mathematical Research (INSPEM), Universiti Putera Malaysia, Selangor, Malaysia^2

Department of Statistics, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran, Indonesia^3

关键词: Computational features;    Numerical experiments;    Numerical results;    Objective function values;    Step size;    Unconstrained optimization;    Unconstrained optimization problems;   

Others  :  https://iopscience.iop.org/article/10.1088/1757-899X/332/1/012024/pdf
DOI  :  10.1088/1757-899X/332/1/012024

来源: IOP

【 摘 要 】

Steepest Descent is known as the simplest gradient method. Recently, many researches are done to obtain the appropriate step size in order to reduce the objective function value progressively. In this paper, the properties of steepest descent method from literatures are reviewed together with advantages and disadvantages of each step size procedure. The development of steepest descent method due to its step size procedure is discussed. In order to test the performance of each step size, we run a steepest descent procedure in C++ program. We implemented it to unconstrained optimization test problem with two variables, then we compare the numerical results of each step size procedure. Based on the numerical experiment, we conclude the general computational features and weaknesses of each procedure in each case of problem.