一般二次规划的一种分解算法

A Decomposition Algorithm for General Quadratic Programming

提出了求解一般二次规划问题的一种分解迭代算法.算法的主要思想是对问题的Hessian矩阵G进行正则分裂,即G=N+H并且满足N-H是正定的.在每次迭代中用一个易于求解的矩阵N代替G进行计算.在矩阵G是正定的条件下,算法具有线性收敛性质,产生的迭代点列收敛到原问题的最优解.当矩阵G不正定时,算法产生的点列收敛到问题的稳定点.

In this paper, the author presents a decomposition iterative algorithm for solving general quadratic programming problem. The main ideas of the algorithm are to split the Hessian matrix G of the problem into the sum of two matrices N and H such that G = N＋ H and N- H is symmetric positive definite matrix. The author uses H which is easier to solve to replace G in each iteration. The se- quence is generated by the algorithm converges to the optimal solution and has a linear rate of convergence if the matrix G is positive definite,or to a stationary point when the matrix G is indefinite.