Regular Splitting and Potential Reduction Method for Solving Quadratic Programming Problem with Box Constraints (Journal of Computational Mathematics, 2021)
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 $ε$-minimum solution or an $ε$-KKT solution by the algorithm is bounded by $O(\frac{n^2}{ε}\log{\frac{1}{ε}}+n\log{(1+\sqrt{2n})})$, and the total running time is bounded by $O(n^2(n+\log n+\log \frac{1}{ε})(\frac{n}{ε}\log{\frac{1}{ε}}+\log n))$ arithmetic operations.