الملخص
A class of damped quasi-Newton methods for nonlinear optimization has recently been proposed by extending the damped-technique of Powell for the BFGS method to the Broyden family of quasi-Newton methods. It has been shown that this damped class has the global and superlinear convergence property that a restricted class of 'undamped' methods has for convex objective functions in unconstrained optimization. To test this result, we applied several members of the Broyden family and their corresponding damped methods to a simple quadratic function and observed several useful features of the damped-technique. These observations and other numerical experiences are described in this paper. The important role of the damped-technique is shown not only for enforcing the above convergence property, but also for improving the performance of efficient, inefficient and divergent undamped methods substantially (significantly in the latter case). Thus, some appropriate ways for employing the damped-technique are suggested.
الكلمات المفتاحية
بيانات النشر
- المعرّف الرقمي
- 10.24200/squjs.vol17iss1pp1-11
- المجلة
- مجلة جامعة السلطان قابوس للعلوم, 16, 1
- الناشر
- جامعة السلطان قابوس
- وصول مفتوح
- وصول مفتوح ذهبي
- الترخيص
- CC BY 4.0
اقتبس هذه المقالة
APA 7
Al‐Baali, M., & Purnama, A. (2012). Numerical Experience with Damped Quasi-Newton Optimization Methods when the Objective Function is Quadratic. Sultan Qaboos University Journal for Science, 16, 1. https://doi.org/10.24200/squjs.vol17iss1pp1-11
MLA 9
Al‐Baali, Mehiddin, and Anton Purnama. "Numerical Experience with Damped Quasi-Newton Optimization Methods when the Objective Function is Quadratic." Sultan Qaboos University Journal for Science, vol. 16, 2012, pp. 1. https://doi.org/10.24200/squjs.vol17iss1pp1-11.
شيكاغو (المؤلف–التاريخ)
Al‐Baali, Mehiddin, and Anton Purnama. 2012. "Numerical Experience with Damped Quasi-Newton Optimization Methods when the Objective Function is Quadratic." Sultan Qaboos University Journal for Science 16: 1. https://doi.org/10.24200/squjs.vol17iss1pp1-11.
هارفارد
Al‐Baali, M. and Purnama, A. (2012) 'Numerical Experience with Damped Quasi-Newton Optimization Methods when the Objective Function is Quadratic', Sultan Qaboos University Journal for Science, 16, pp. 1. doi:10.24200/squjs.vol17iss1pp1-11.
فانكوفر
Al‐Baali M, Purnama A. Numerical Experience with Damped Quasi-Newton Optimization Methods when the Objective Function is Quadratic. Sultan Qaboos University Journal for Science. 2012;16:1. doi:10.24200/squjs.vol17iss1pp1-11
IEEE
M. Al‐Baali, and A. Purnama, "Numerical Experience with Damped Quasi-Newton Optimization Methods when the Objective Function is Quadratic," Sultan Qaboos University Journal for Science, vol. 16, pp. 1, 2012, doi: 10.24200/squjs.vol17iss1pp1-11.