Hidayatullah, Alvian Alif (2024) Pendekatan Metode Proyeksi Himpunan Konveks Dalam Menyelesaikan Model Homogeneous Self-Dual Dari Permasalahan Quadratically Constrained Linear Programming (Studi Kasus: Optimasi Portofolio). Masters thesis, Institut Teknologi Sepuluh Nopember.
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Abstract
Optimasi matematika merupakan konsep matematika yang didasarkan pada pemilihan elemen terbaik dengan memperhatikan beberapa kriteria dari beberapa rangkaian alternatif yang tersedia. Beberapa konsep yang telah dikembangkan, seperti permasalahan quadratically constrained linear programming (QCLP) memberikan konsep alternatif dalam menyelesaikan permasalahan optimasi matematika. Seperti menyelesaikan permasalahan optimasi portofolio berdasarkan model QCLP. Pada Tesis ini diselesaikan permasalahan QCLP dengan pendekatan optimasi matematika. Konsep permasalahan QCLP yang akan diselesaikan didasarkan pada bentuk model Homogeneous Self-Dual (HSD) dari permasalahan QCLP. Penyelesaian model HSD pada QCLP ini menggunakan pendekatan metode proyeksi terhadap himpunan konveks (POCS: projection onto convex set), averaged projection dan Dykstra's projection. Pada Tesis ini, permasalahan optimasi portofolio menjadi studi kasus dari permasalahan QCLP. Permasalahan optimasi portofolio dianalisis berdasarkan nilai konvergensi dari metode POCS, averaged projection dan Dykstra's projection pada solusi primal dan solusi dual dari model HSD. Selanjutnya dari hasil analisis tersebut, dilakukan simulasi numerik untuk membandingkan tiga metode tersebut berdasarkan nilai konvergensi dari solusi primal dan solusi dual dari model HSD permasalahan optimasi portofolio. Simulasi pada Tesis ini menggunakan Cauchy stopping criteria dan projection criteria sebagai stopping criteria
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Mathematical optimization is a mathematical concept based on the selection of the best element by considering several criteria from several sets of available alternatives. Some concepts that have been developed, such as the quadratically constrained linear programming (QCLP) problem, provide alternative concepts in solving mathematical optimization problems. Such as solving portfolio optimization problems based on the QCLP model. In this thesis, the QCLP problem is solved with a mathematical optimization approach. The concept of the QCLP problem to be solved is based on the form of the model Homogeneous Self-Dual (HSD) of the QCLP problem. The solution of the HSD model in QCLP uses projection onto convex set (POCS), averaged projection and Dykstra's projection. In this thesis, the portfolio optimization problem becomes a case study of the QCLP problem. The portfolio optimization problem is analyzed based on the convergence value of the POCS, averaged projection and Dykstra's projection methods on the primal solution and the dual solution of the HSD model. Furthermore, from the results of the analysis, numerical simulations are carried out to compare the three methods based on the convergence value of the primal solution and the dual solution of the HSD model of portfolio optimization problems. The simulation in this thesis uses Cauchy stopping criteria and projection criteria as stopping criteria
| Item Type: | Thesis (Masters) |
|---|---|
| Uncontrolled Keywords: | Quadratically constrained linear programming, Homogeneous Self-Dual, projection onto convex sets, averaged projection, Dykstra’s projection, optimasi portofolio, Cauchy stopping criteria, projection criteria |
| Subjects: | Q Science > QA Mathematics > QA11 .A36 1991 Mathematics--Study and teaching. Q Science > QA Mathematics > QA401 Mathematical models. Q Science > QA Mathematics > QA611.28 Metric spaces Q Science > QA Mathematics > QA9.58 Algorithms |
| Divisions: | Faculty of Science and Data Analytics (SCIENTICS) > Mathematics > 44101-(S2) Master Thesis |
| Depositing User: | Alvian Alif Hidayatullah |
| Date Deposited: | 12 Feb 2024 02:21 |
| Last Modified: | 12 Feb 2024 02:21 |
| URI: | http://repository.its.ac.id/id/eprint/106431 |
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