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A New Hybrid Conjugate Gradient Method Based on Eigenvalue Analysis for Unconstrained Optimization Problems | ||
| Control and Optimization in Applied Mathematics | ||
| مقاله 2، دوره 3، شماره 1، مهر 2018، صفحه 27-43 اصل مقاله (532.11 K) | ||
| نوع مقاله: Research Article | ||
| شناسه دیجیتال (DOI): 10.30473/coam.2019.44564.1108 | ||
| نویسندگان | ||
| Farzad Rahpeymaii* 1؛ majid rostami2 | ||
| 1Department of Mathematics, Payame Noor University, PO BOX 19395-3697, Tehran, Iran | ||
| 2Young Researchers and Elite Club‎, ‎Hamedan Branch‎, ‎Islamic Azad University‎, ‎Hamedan‎, ‎Iran | ||
| چکیده | ||
| In this paper, two extended three-term conjugate gradient methods based on the Liu-Storey ({\tt LS}) conjugate gradient method are presented to solve unconstrained optimization problems. A remarkable property of the proposed methods is that the search direction always satisfies the sufficient descent condition independent of line search method, based on eigenvalue analysis. The global convergence of proposed algorithms is established under suitable conditions. Preliminary numerical results show that the proposed methods are efficient and robust to solve the unconstrained optimization problems. | ||
| کلیدواژه‌ها | ||
| Unconstrained optimization؛ Conjugate gradient methods؛ Eigenvalue analysis؛ Global convergence؛ Numerical comparisons | ||
| عنوان مقاله [English] | ||
| یک روش گرادیان مزدوج ترکیبی جدید بر پایه آنالیز مقادیر ویژه برای مسائل بهینه‌سازی نامقید | ||
| نویسندگان [English] | ||
| فرزاد راهپیمایی1؛ مجید رستمی2 | ||
| چکیده [English] | ||
| در این مقاله، دو روش گرادیان مزدوج سه‌جمله‌ای تعمیم‌یافته بر پایه روش گرادیان مزدوج لیو-استوری برای حل مسائل بهینه‌سازی نامقید ارائه شده است. ویژگی مهم و اصلی روش‌های جدید، تولید جهت‌های جستجوی کاهشی بر پایه آنالیز مقادیر ویژه و مستقل از نوع جستجوی خطی است. همگرایی سراسری الگوریتم‌های جدید ارائه شده تحت برخی فرض‌های مناسب اثبات شده است. نتایج عددی نشان می‌دهند که روش‌های پیشنهادی برای حل مسائل بهینه‌سازی نامقید کارا و قوی هستند. | ||
| کلیدواژه‌ها [English] | ||
| بهینه‌سازی نامقید, روش‌های گرادیان مزدوج, آنالیز مقادیر ویژه, همگرایی سراسری, مقایسه‌های عددی | ||
| مراجع | ||
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