A DERIVATIVE-FREE ALGORITHM FOR LEAST-SQUARES MINIMIZATION

作者：Zhang Hongchao^*; Conn Andrew R; Scheinberg Katya

来源：SIAM Journal on Optimization, 2010, 20(6): 3555-3576.

DOI：10.1137/09075531X

• derivative-free optimization
• least-squares
• trust region
• Levenberg-Marquardt method
• system of nonlinear equations
• global convergence

We develop a framework for a class of derivative-free algorithms for the least-squares minimization problem. These algorithms are designed to take advantage of the problem structure by building polynomial interpolation models for each function in the least-squares minimization. Under suitable conditions, global convergence of the algorithm is established within a trust region framework. Promising numerical results indicate the algorithm is both efficient and robust. Numerical comparisons are made with standard derivative-free software packages that do not exploit the special structure of the least-squares problem or that use finite differences to approximate the gradients.

• 出版日期2010