Regular Splitting and Potential Reduction Method for Solving Quadratic Programming Problem with Box Constraints

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 $\epsilon$-minimum solution or 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.