On limited memory SQP methods for large scale constrained nonlinear least squares problems

Z. F. Li


This paper describes limited memory Sequential Quadratic Programming methods (LSQP) for a large scale equality constrained nonlinear least squares problem. By introducing additional variables, the original problem is transformed into a general equality constrained nonlinear programming problem with a simple objective. This is then solved by a limited memory variation of SQP methods. This overcomes one of the major drawbacks of the traditional SQP method, where a large matrix needs to be stored, and combines the best performance of the Gauss-Newton and Quasi-Newton methods by a suitable choice of the Lagrangian Hessian approximation. Our numerical tests indicate that the new method is faster than the reduced Hessian (RSQP) method, and is better able to use additional storage to accelerate convergence. For some problems it approaches the performance of the full Hessian SQP (FSQP) method adapted for least squares problems in Schittkowski. However, his method cannot cope with problems with very many observations.

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DOI: http://dx.doi.org/10.21914/anziamj.v42i0.627

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ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.