A Decomposition method for solving quadratic programming (QP) with boxconstraints is presented in this paper. It is similar to the iterative method forsolving linear system of equations. The main ideas of the algorith...A Decomposition method for solving quadratic programming (QP) with boxconstraints is presented in this paper. It is similar to the iterative method forsolving linear system of equations. The main ideas of the algorithm are to splitthe Hessian matrix Q of the oP problem into the sum of two matrices N and Hsuch that Q = N + H and (N - H) is symmetric positive definite matrix ((N, H)is called a regular splitting of Q)[5]. A new quadratic programming problem withHessian matrix N to replace the original Q is easier to solve than the originalproblem in each iteration. The convergence of the algorithm is proved under certainassumptions, and the sequence generated by the algorithm converges to optimalsolution and has a linear rate of R-convergence if the matrix Q is positive definite,or a stationary point for the general indefinite matrix Q, and the numerical resultsare also given.展开更多
文摘A Decomposition method for solving quadratic programming (QP) with boxconstraints is presented in this paper. It is similar to the iterative method forsolving linear system of equations. The main ideas of the algorithm are to splitthe Hessian matrix Q of the oP problem into the sum of two matrices N and Hsuch that Q = N + H and (N - H) is symmetric positive definite matrix ((N, H)is called a regular splitting of Q)[5]. A new quadratic programming problem withHessian matrix N to replace the original Q is easier to solve than the originalproblem in each iteration. The convergence of the algorithm is proved under certainassumptions, and the sequence generated by the algorithm converges to optimalsolution and has a linear rate of R-convergence if the matrix Q is positive definite,or a stationary point for the general indefinite matrix Q, and the numerical resultsare also given.
