IMPROVED PROJECTED GRADIENT ALGORITHMS FOR SINGLY LINEARLY CONSTRAINED QUADRATIC PROGRAMS SUBJECT TO LOWER AND UPPER BOUNDS

Yun-Shan Fu and Yu-Hong Dai ()
Additional contact information
Yun-Shan Fu: LSEC, ICMSEC, Academy of Mathematics & Systems Science, Chinese Academy of Sciences, P.O. Box 2719, Beijing 100080, China
Yu-Hong Dai: LSEC, ICMSEC, Academy of Mathematics & Systems Science, Chinese Academy of Sciences, P.O. Box 2719, Beijing 100080, China

Asia-Pacific Journal of Operational Research (APJOR), 2010, vol. 27, issue 01, 71-84

Abstract: In this paper, we consider the projected gradient algorithms for solving the quadratic program with bound constraints and a single linear equality constraint (SLBQP). We establish the relationship between the Lagrangian multiplier in the projection subproblem and the Lagrangian multiplier in the original optimization problem. Then we give an improved initial estimate of the Lagrangian multiplier in the subproblem based on this relationship. It appears that this initial estimate is very close to the optimal Lagrangian multiplier after several iterations of the outer loop. This will reduce at most 40% of the computing time in the projection subproblem. This initial guess can also be used in all kinds of projected gradient methods for solving the SLBQP problem. The numerical results show that it brings much more improvement in monotone algorithms than in nonmonotone algorithms. We also apply the adaptive steepest descent step-size and the Dai-Yuan step-size which are two monotone step-sizes to the projected gradient method of this SLBQP problem. Our numerical experiments showed that their performance can be better than some other monotone projected gradient methods.

Keywords: Monotone projected gradient algorithm; Support Vector Machine (SVM); adaptive steepest descent step-size; Dai-Yuan step-size; projection subproblem (search for similar items in EconPapers)
Date: 2010
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.worldscientific.com/doi/abs/10.1142/S0217595910002594
Access to full text is restricted to subscribers

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wsi:apjorx:v:27:y:2010:i:01:n:s0217595910002594

Ordering information: This journal article can be ordered from

DOI: 10.1142/S0217595910002594

Access Statistics for this article

Asia-Pacific Journal of Operational Research (APJOR) is currently edited by Gongyun Zhao

More articles in Asia-Pacific Journal of Operational Research (APJOR) from World Scientific Publishing Co. Pte. Ltd.
Bibliographic data for series maintained by Tai Tone Lim ().