改进共轭梯度法求解无约束二次凸规划问题

The Improved Conjugate Gradient Method for Solving the Unconstrained Convex Quadratic Programming Problem

针对共轭梯度法求解无约束二次凸规划时,在构造共轭方向上的局限性,对共轭梯度法进行了改进.给出了构造共轭方向的新方法,利用数学归纳法对新方法进行了证明.同时还给出了改进共轭梯度法在应用时的基本计算过程,并对方法的收敛性进行了证明.通过实例求解,说明了在求解二次无约束凸规划时,该方法相比共轭梯度法具有一定的优势.

When the unconstrained convex quadratic programming problem is solved by the conjugate gradient, themethod has limitation in constructing the conjugate directions. The paper gives an improved conjugate gradient method forconstructiong the conjugate directions, and uses the mathematical induction to prove the method, and gives the calculationsteps, and the convergence of the new method is proved, through solving the example, the method has some advantagescompared to the conjugate gradient.