ABSTRACT

We propose structured spectral gradient algorithms for solving nonlinear least squares problems based on a modified structured secant equation. The idea was to integrate more details of the Hessian of the objective function into the standardized spectral parameters with the goal of improving numerical efficiency. We safeguard the structured spectral parameters to avoid negative curvature search direction. The sequence of the search direction generated by the respective proposed algorithm satisfies the sufficient descent condition. Using a nonmonotone line search strategy, we establish the global convergence of the proposed algorithms under some standard assumptions. Numerical experiments on some benchmark test problems show that the proposed algorithms are efficient and outperform some existing competitors.

摘要

我们提出了一种结构化谱梯度算法，用于基于改进的结构化割线方程求解非线性最小二乘问题。目的是将目标函数的Hessian的更多细节集成到标准化的光谱参数中，以提高数值效率。我们保护结构化的光谱参数，以避免负曲率搜索方向。由各自提出的算法生成的搜索方向的序列满足足够的下降条件。使用非单调线搜索策略，我们在某些标准假设下建立了所提出算法的全局收敛性。对一些基准测试问题的数值实验表明，所提出的算法是有效的，并且优于某些现有竞争者。