Convergence of a Regularized Euclidean Residual Algorithm for Nonlinear Least-Squares
Convergence of a Regularized Euclidean Residual Algorithm for Nonlinear Least-Squares
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DOI：
10.1137/080732432
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发表时间：
2010-04
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影响因子：
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通讯作者：
S. Bellavia;C. Cartis;N. Gould;B. Morini;P. Toint
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文献类型：
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作者：
S. Bellavia;C. Cartis;N. Gould;B. Morini;P. Toint
研究了求解一般非线性最小二乘和非线性方程问题的新正则化欧氏残量法的收敛性。这种方法，来自Nesterov [Optim.方法采用计算机软件，22（2007），pp. 469-483]，使用由二次项正则化的非平方欧几里德线性化残差组成的目标函数的模型。与以前的分析不同，它的收敛性在这里被认为是没有假设一致非奇异的全局Lipschitz连续雅可比矩阵，也没有一个精确的子问题的解决方案。证明了该方法对一阶临界点是全局收敛的，在更强的假设下，对非线性方程组的根也是全局收敛的。收敛速度也被证明是二次更强的假设下。
The convergence properties of the new regularized Euclidean residual method for solving general nonlinear least-squares and nonlinear equation problems are investigated. This method, derived from a proposal by Nesterov [Optim. Methods Softw., 22 (2007), pp. 469-483], uses a model of the objective function consisting of the unsquared Euclidean linearized residual regularized by a quadratic term. At variance with previous analysis, its convergence properties are here considered without assuming uniformly nonsingular globally Lipschitz continuous Jacobians nor an exact subproblem solution. It is proved that the method is globally convergent to first-order critical points and, under stronger assumptions, to roots of the underlying system of nonlinear equations. The rate of convergence is also shown to be quadratic under stronger assumptions.