Metode Quasi-Newton Menggunakan Formula Powell-Symmetric-Broyden (PSB) Dan Symmetric-Rank-One (SR 1)

Agustin, Winda (2013) Metode Quasi-Newton Menggunakan Formula Powell-Symmetric-Broyden (PSB) Dan Symmetric-Rank-One (SR 1). Sarjana thesis, Universitas Brawijaya.

Abstract

Metode Quasi-Newton merupakan salah satu metode untuk menyelesaikan masalah optimasi fungsi nonlinear tanpa kendala. Dalam skripsi ini, metode Quasi-Newton yang digunakan adalah formula Powell-Symmetric-Broyden (PSB) dan Symmetric-Rank-One (SR 1) dengan pendekatan invers matriks Hessian. Contoh kasus yang digunakan untuk menentukan nilai minimum fungsi dua variabel tanpa kendala, diaplikasikan pada fungsi unimodal, yaitu pada tes fungsi kuadrat. Berdasarkan tes fungsi kuadrat yang diuji, nilai minimum yang dihasilkan dari formula Powell-Symmetric-Broyden (PSB) sebesar 0.809589 x 10-10, 0.166878 x 10-10, dan -132.333333326 3433000, serta formula Symmetric-Rank-One (SR 1) sebesar 0.809588 x 10-10, 0.166877 x 10-10, dan -132.3333333263437000. Nilai minimum dari kedua formula tersebut telah mendekati nilai yang sebenarnya. Berdasarkan galat mutlak dan galat relatif hampirannya, nilai minimum yang dihasilkan dari formula Symmetric-Rank-One (SR 1) lebih mendekati nilai yang sebenarnya daripada nilai minimum yang dihasilkan dari formula Powell-Symmetric-Broyden (PSB). Dengan hasil nilai minimum yang mendekati nilai sebenarnya, jumlah iterasi yang diperlukan dari formula Powell-Symmetric-Broyden (PSB) relatif sama dengan formula Symmetric-Rank-One (SR 1).

English Abstract

Quasi-Newton method is one of method to solve the problem of a nonlinear function without constraints. In this thesis, Powell-Symmetric-Broyden (PSB) and Symmetric-Rank-One (SR 1) formula with inverse Hessian matrix approach is used Quasi-Newton method. The examples of cases that used to specify the minimum values of two variables functions without the constraints, applied to unimodal function, which is the test of quadratic functions. Based on the test of tested quadratic function, the minimum value that generated by Powell-Symmetric-Broyden (PSB) formula is 0.809589 x 10-10, 0.166878 x 10-10, and -132.3333333263433000, and Symmetric-Rank-One (SR 1) formula is 0.809588 x 10-10, 0.166877 x 10-10, and -132.3333333263437000. The minimum value from both formulas have approached the actual value. Based on the absolute error and relative error of the approximation, the minimum value is generated by Symmetric-Rank-One (SR 1) formula is closer to the actual value than Powell-Symmetric-Broyden (PSB) formula with the minimum value that approximates the actual value, number of iterations takes Powell-Symmetric-Broyden (PSB) formula is similar with Symmetric-Rank-One (SR 1) formula

Item Type:	Thesis (Sarjana)
Identification Number:	SKR/MIPA/2013/240/051307220
Subjects:	500 Natural sciences and mathematics > 510 Mathematics
Divisions:	Fakultas Matematika dan Ilmu Pengetahuan Alam > Matematika
Depositing User:	Hasbi
Date Deposited:	05 Sep 2013 09:40
Last Modified:	25 Oct 2021 01:55
URI:	http://repository.ub.ac.id/id/eprint/153500

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