Volume 20, Issue 6
Regular Splitting and Potential Reduction Method for Solving Quadratic Programming Problem with Box Constraints
DOI:

J. Comp. Math., 20 (2002), pp. 643-652

Published online: 2002-12

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• Abstract

A regular splitting and potential reduction method is presented for solving a quadratic programming problem with box constraints (QPB) in this paper. A general algorithm is designed to solve the QPB problem and generate a sequence of iterative points. We show that the number of iterations to generate an $\epsilon-KKT$ solution by the algorithm is bounded by $O(\frac{n^2}{\epsilon}\log{\frac{1}{\epsilon}}+n\log{(1+\sqrt{2n})})$, and the total running time is bounded by $O(n^2(n+\log n+\log \frac{1}{\epsilon})(\frac{n}{\epsilon}\log{\frac{1}{\epsilon}}+\log n))$ arithmetic operations.

• Keywords

Quadratic programming problem Regular splitting Potential reduction algorithm Complex

• AMS Subject Headings

@Article{JCM-20-643, author = {}, title = {Regular Splitting and Potential Reduction Method for Solving Quadratic Programming Problem with Box Constraints}, journal = {Journal of Computational Mathematics}, year = {2002}, volume = {20}, number = {6}, pages = {643--652}, abstract = { A regular splitting and potential reduction method is presented for solving a quadratic programming problem with box constraints (QPB) in this paper. A general algorithm is designed to solve the QPB problem and generate a sequence of iterative points. We show that the number of iterations to generate an $\epsilon-KKT$ solution by the algorithm is bounded by $O(\frac{n^2}{\epsilon}\log{\frac{1}{\epsilon}}+n\log{(1+\sqrt{2n})})$, and the total running time is bounded by $O(n^2(n+\log n+\log \frac{1}{\epsilon})(\frac{n}{\epsilon}\log{\frac{1}{\epsilon}}+\log n))$ arithmetic operations. }, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8949.html} }
TY - JOUR T1 - Regular Splitting and Potential Reduction Method for Solving Quadratic Programming Problem with Box Constraints JO - Journal of Computational Mathematics VL - 6 SP - 643 EP - 652 PY - 2002 DA - 2002/12 SN - 20 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8949.html KW - Quadratic programming problem KW - Regular splitting KW - Potential reduction algorithm KW - Complex AB - A regular splitting and potential reduction method is presented for solving a quadratic programming problem with box constraints (QPB) in this paper. A general algorithm is designed to solve the QPB problem and generate a sequence of iterative points. We show that the number of iterations to generate an $\epsilon-KKT$ solution by the algorithm is bounded by $O(\frac{n^2}{\epsilon}\log{\frac{1}{\epsilon}}+n\log{(1+\sqrt{2n})})$, and the total running time is bounded by $O(n^2(n+\log n+\log \frac{1}{\epsilon})(\frac{n}{\epsilon}\log{\frac{1}{\epsilon}}+\log n))$ arithmetic operations.