A numerically stable least squares solution to the quadratic programming problem |
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Authors: | E Übi |
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Institution: | (1) Department of Economics, Tallinn University of Technology, Kopli 101, 11712 Tallinn, Estonia |
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Abstract: | The strictly convex quadratic programming problem is transformed to the least distance problem — finding the solution of minimum
norm to the system of linear inequalities. This problem is equivalent to the linear least squares problem on the positive
orthant. It is solved using orthogonal transformations, which are memorized as products. Like in the revised simplex method,
an auxiliary matrix is used for computations. Compared to the modified-simplex type methods, the presented dual algorithm
QPLS requires less storage and solves ill-conditioned problems more precisely. The algorithm is illustrated by some difficult
problems.
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Keywords: | Quadratic programming system of linear inequalities method of least squares Householder transformation successive projection |
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