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A comparison of block pivoting and interior-point algorithms for linear least squares problems with nonnegative variables

Authors: Luís F. Portugal, Joaquím J. Júdice and Luís N. Vicente
Journal: Math. Comp. 63 (1994), 625-643
MSC: Primary 90C20; Secondary 65K05
MathSciNet review: 1250776
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Abstract: In this paper we discuss the use of block principal pivoting and predictor-corrector methods for the solution of large-scale linear least squares problems with nonnegative variables (NVLSQ). We also describe two implementations of these algorithms that are based on the normal equations and corrected seminormal equations (CSNE) approaches. We show that the method of normal equations should be employed in the implementation of the predictor-corrector algorithm. This type of approach should also be used in the implementation of the block principal pivoting method, but a switch to the CSNE method may be useful in the last iterations of the algorithm. Computational experience is also included in this paper and shows that both the predictor-corrector and the block principal pivoting algorithms are quite efficient to deal with large-scale NVLSQ problems.

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Keywords: Least squares problems, linear complementarity problem, quadratic programming, sparse matrices, large-scale optimization
Article copyright: © Copyright 1994 American Mathematical Society