TY - JOUR
T1 - Regular Splitting and Potential Reduction Method for Solving Quadratic Programming Problem with Box Constraints
AU - Wei , Zi-Luan
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, Regular splitting, Potential reduction algorithm, Complexity analysis.
AB - <p style="text-align: justify;">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&nbsp;<span style="text-align: justify;">$\epsilon$-minimum solution or</span> 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.</p>