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A conic Newton method is attractive because it converges to a local minimizzer rapidly from any sufficiently good initial guess. However, it may be expensive to solve the conic Newton equation at each iterate. In this paper we consider an inexact conic Newton method, which solves the couic Newton equation oldy approximately and in sonm unspecified manner. Furthermore, we show that such method is locally convergent and characterizes the order of convergence in terms of the rate of convergence of the relative residuals. 相似文献
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考虑非线性规划问题:[1]和[4]曾讨论对某点x处的投影Hesse阵z(x)~T?_(xx)~2L(x,λ)z(x)进行变尺度校正算法的收敛性.假设f(x),c_i(x),i=1,…,t为二次连续可微函数,x~*为(1.1)的解,且在x~*处满足二阶充分性条件,以及假设 相似文献
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解线性不等式组的松弛直交变换法 总被引:1,自引:0,他引:1
盛松柏 《高等学校计算数学学报》1990,(4)
求解线性不等式组已有许多方法。本文利用直交变换将原线性不等式组之解集变换成一个r维平面与正锥之交集,然后采用松弛直交投影法。在采用加速方法后,很快就能求得一个解。这不但可以解相容线性不等式组,还可以方便地判别线性不等式组不相容。数值试验表明,本文提出的方法相当有效。 本文在§2中介绍计算公式,收敛性分析放在§3。加速方法和初始点的选取分别在§4和§5中叙述。算法见§6,然后介绍数值试验情况。最后一节将介绍本文的方法可以改善坏条件问题,以及怎样用新方法寻找线性规划的初始可行点。 相似文献
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An algorithm for solving nonlinear least squares problems with general linear inequality constraints is described.At each step,the problem is reduced to an unconstrained linear least squares problem in a subs pace defined by the active constraints,which is solved using the quasi-Newton method.The major update formula is similar to the one given by Dennis,Gay and Welsch (1981).In this paper,we state the detailed implement of the algorithm,such as the choice of active set,the solution of subproblem and the avoidance of zigzagging.We also prove the globally convergent property of the algorithm. 相似文献
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This paper is concerned with the solution of the nonlinear least squares problems. A new secant method is suggested in this paper, which is based on an affine model of the objective function and updates the first-order approximation each step when the iterations proceed. We present an algorithm which combines the new secant method with Gauss-Newton method for general nonlinear least squares problems. Furthermore, we prove that this algorithm is Q-superlinearly convergent for large residual problems under mild conditions. 相似文献
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盛松柏 《高等学校计算数学学报(英文版)》1997,(2)
A Class of Collinear Scaling Algorithms for Unconstrained Optimization. An appealing approach to the solution of nonlinear optimization problems based on conic models of the objective function has been in troduced by Davidon (1980). It leads to a broad class of algorithms which can be considered to generalize the existing quasi-Newton methods. One particular member of this class has been deeply discussed by Sorensen (1980), who has proved some interesting theoretical properties. In this paper, we generalize Sorensen's technique to Spedicato three-parameter family of variable-metric updates. Furthermore, we point out that the collinear scaling three- parameter family is essentially equivalent to the Spedicato three-parameter family. In addition, numerical expriments have been carried out to compare some colliner scaling algorithms with a straightforward implementation of the BFGS quasi-Newton method. 相似文献
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盛松柏 《高等学校计算数学学报(英文版)》1995,(1)
For satate form linear gram as Fang and sao deined and approach which would find an optimal solution by solving an anconstrained convex dual programming.Thedual was construcied by applying an emropic peturbation and a simple Inequality Inz0n,In this paper,we suggest than a paperbation functiontake the place of Inx such that the new approdt has good numerical stability andhas all properties of the original method 相似文献
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