PERBANDINGAN HASIL NUMERIK METODE KONJUGAT GRADIEN HIBRID BARU (LS-DY) DAN METODE HS-CD

Authors

  • T Murdani Saputra Universitas Syiah Kuala
  • Ikhsan Maulidi Universitas Syiah Kuala
  • Radhiah Radhiah Universitas Syiah Kuala

DOI:

https://doi.org/10.24252/msa.v10i1.26901

Abstract

Metode konjugat gradien merupakan suatu metode untuk menyelesaikan sistem persamaan linier pada skala besar, yang mana metode tersebut diperkenalkan oleh Hestenes dan Stiefel untuk menyelesaikan permasalahan tersebut. Metode konjugat gradien merupakan metode iteratif dan juga merupakan salah satu metode yang efektif dalam menyelesaikan optimasi tak berkendala. Dalam tulisan ini, penulis melakukan pengusulan metode konjugat gradien hibrid baru berdasarkan ide dari metode NH1, NH2, NH3 dan NH4. Metode hibrid tersebut diusulkan berdasarkan dari kekurangan dan kelebihan dari metode sebelumnya yaitu metode HS, FR, PRP, CD, LS dan Metode DY. Kekurangan dan kelebihan dari metode-metode tersebut diantaranya proses kinerja komputasi (iterasi) kurang baik dan kekonvergenan global. Berdasarkan dari metode-metode hibrid yang diusulkan tersebut maka penulis mengusulkan metode baru yaitu penggabungan dari metode LS dengan metode DY, dimana metode LS memiliki kelebihan pada kinerja komputasi dan DY kelebihannya pada kekonvergenan globalnya. Metode hibrid baru yang diusulkan tersebut yaitu metode NH5 (LS-DY) dan metode yang diusulkan ini akan di ujikan pada fungsi tak linear orde tinggi. Metode baru menunjukkan bahwa fungsi-fungsi yang diberikan dapat diselesaikan dengan sangat efisien serta perbandingan metode NH5 dengan metode-metode sebelumnya menunjukkan hasil pada proses komputasinya baik dan dapat bersaing

Kata Kunci: metode konjugat gradien, metode hibrid, knerja komputasi.

References

[1] Nocedal, J., & Wright, SJ. (1999). Numerical Optimization. New York: Springer-Verlag.
[2] Hestenes, MR., Stiefel EL. (1952). Methods of Conjugate Gradient for Solving Linear System. Journal of Research of the Nattional Bureau of Standart. 49(6): 409-432.
[3] Fletcher, R., & Reeves, C. (1964). Function Minimazation by Conjugate Gradient. The Computer Journal, 7:149 – 154.
[4] Polak, B., Ribiѐre, G. (1969). Note Surla Convergence des Méthodes de Directions Conjuguées. Francaise Imformat Recherche Opertionelle, 16:35–43.
[5] Polyak, BT. (1969). The Conjugate Gradient Method in Extreme Problems, USSR Computational Mathematics and Mathematical Physics, 9(4): 94-112.
[6] Fletcher, R, (1987). Practical Methods of Optimization, Unconstrained Optimization. New York: Wiley.
[7] Liu, YL., & Storey, CS. (1991). Efficient Generalized Conjugate Gradient Algorithms, Part 1: Theory. Journal of Optimization Theory and Applications, 69(1):129-137.
[8] Dai, YH., & Yuan, Y. (1999). A Nonlinear Conjugate Gradient Method with a Strong Global Convergence Property. SIAM Journal on Optimization, 10: 177-182.
[9] Touati-Ahmed, D., & Storey, C. (1990). Efficient Hybrid Conjugate Gradient Techniques: Journal of Optimization Theory and Applications, 64(2): 379–397.
[10] Zhang, L., & Zhou, W. (2007). Two Descent Hybrid Conjugate Method for Optimazation. Journal of Computational and Applied Mathematics, 216:251-264.doi: 10.1016/j.cam.2007. 04.028.
[11] Zhou, A., Zhu, Z., Fan, H., & Qing, Q. (2011). Three New Hybrid Conjugate Gradient Method for Optimazation. Applied Mathematics, 2:303-308.doi: 10.4236/am.2011.23035.
[12] Saputra, T. Murdani., Silalahi, Bib Paruhum., & Guritman, Sugi. (2020). Metode Konjugat Gradien Hibrid Baru: Metode HS-CD Untuk Menyelesaikan Masalah Optimasi Tak Berkendala. Journal Matematika dan Statistika serta Aplikasinya, 8:37-45. doi: 10.24252/msav8i1.12294.
[13] Andrei, N. (2008). An Unconstrained Optimization Test Function Collection. Advanced Modelling and Optimization, 10(1): 147-161.
[14] Dolan, JED., & Morѐ, JJ. (2002). Benchmarking Optimization Sofware with Performance Profil. Mathematical Programming. 912(2): 201-213.doi: 10.1007/s101070100263

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Published

2022-06-14

How to Cite

[1]
T. M. Saputra, I. Maulidi, and R. Radhiah, “PERBANDINGAN HASIL NUMERIK METODE KONJUGAT GRADIEN HIBRID BARU (LS-DY) DAN METODE HS-CD”, MSA, vol. 10, no. 1, pp. 47–52, Jun. 2022.

Issue

Vol. 10 No. 1 (2022): VOLUME 10 NOMOR 1 TAHUN 2022

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Artikel

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