A Derivative-Free Algorithm for Least-Squares Minimization

Authors:
Hongchao Zhang;Andrew R. Conn;Katya Scheinberg
Affiliations:
hozhang@math.lsu.edu;arconn@us.ibm.com;katyascheinberg@gmail.com
Venue:
SIAM Journal on Optimization
Year:
2010

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Abstract

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.