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

DOI:
https://doi.org/10.1090/S0025-5718-1994-1250776-4

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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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1994-1250776-4

Keywords:
Least squares problems,
linear complementarity problem,
quadratic programming,
sparse matrices,
large-scale optimization

Article copyright:
© Copyright 1994
American Mathematical Society