关键词: 计算机寻优, 牛顿法, 共轭梯度法, Hessian矩阵, 梯度

Abstract: A new computational optimization algorithm for unconstrained functions is proposed in this work.The algorithm is expected to cause that Euclidean norm of the gradient of objective function gradually shrinks to zero，in order to minimize the objective function.The new algorithm is named gradient shrink method.It combines the advantages of Newton’s method and conjugate gradient method.It uses second-order derivatives of the objective function，so the convergence rate is rather good，and has the quadratic termination property.When Hessian matrix is singular，Newton’s method will fail to continue，but the disadvantage can be fully avoided in gradient shrink method.In addition，it can quickly determinate whether a saddle point is converged to.

Key words: computational optimization, Newton’s method, conjugate gradient method, Hessian matrix, gradient