【摘要】 针对非线性最小二乘问题,利用锥模型算法思想,给出了海赛矩阵中二阶信息项的割线近似的不同校正公式,并利用自适应信赖域技术给出了求解非线性最小二乘问题的自适应锥模型信赖域算法.算法中我们允许使用非精确方法近似求解信赖域子问题.文中给出了新算法的全局收敛性和超线性收敛性分析以及数值试验结果.更多还原

【Abstract】 In this paper,a new method for nonlinear least-squares problems is presented.The method uses the quasi-Newton update of the Gauss-Newton Hessian based on a conic model.A method with adaptive trust region strategy is constructed.The method needs to solve the trust region subproblem with a conic model,which can be transformed to the trust region subproblem with a quadratic model.So the algorithm is easily implemented.The new algorithm is analyzed and its global and local superlinear convergence results is established.Numerical tests are presented that confirm the efficiency of the new algorithm.更多还原