Pengembangan Metode Steepest Descent pada Optimasi Tanpa Kendala

Abstract

The q-gradient method with the Yuan step size search on odd steps and geomet- ric recursion as the even step size search is called q - GY1. It aimed to speed up convergence to a minimum by minimizing the number of iterations. q-G method is a dilatation of the q parameter to the independent variable by com- paring the results of four algorithms, namely, the classical steepest descent (SD) method, the steepest method with Yuan steps of descent (SDY), the q-gradient method with geometric recursion (q - G), q-gradient method with Yuan step size (q - GY). The presentation of numerical results were in the form of tables and graphs, using the Rosenbrock function f(x)=(1 − x1)2 + 100 × (x2 − x21 )2 deter- mined μ = 1, 0 = 0.5, = 0.999, initial point was generated on the interval x0 = (−2.048, 2.048) and Rastrigin fuction f(x)=An +Pn i=1[x2 i − 10cos(2 xi)] with μ = 1, 0 = 5.0 as a variable to determine the parameters q and = 0.995 as a reduction factor to find the value of the standard deviation in each iteration on the interval x0 = (−5.12, 5.12) in R2. The iteration was run on 49 initial points (x0) using Python online compiler on laptop with 64 bit core i3. The maximum number of iterations is 58.679. Using the tolerance limit as a stopping criterion, namely 10−4 and f(x ) > f. q - GY1 on Rastrigin function did not show conclu- sive results. However, the downward movement towards the minimum point was better than the method SD, SDY dan q - GY while on the Rosenbrock function the numerical results showed a fairly good performance to be able to increase the convergence to a minimum point.