A numerically stable least squares solution to the quadratic programming problem

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 transforma...

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Bibliographic Details
Published in:Central European journal of mathematics Vol. 6; no. 1; pp. 171 - 178
Main Author: Übi, E.
Format: Journal Article
Language:English
Published: Heidelberg SP Versita 01.03.2008
Versita
De Gruyter Brill Sp. z o.o., Paradigm Publishing Services
Subjects:
65K05
90C05
Algebra
Algorithms
Geometry
Householder transformation
Ill-conditioned problems (mathematics)
Least squares method
Lie Groups
Linear functions
Mathematics
Mathematics and Statistics
method of least squares
Number Theory
Probability Theory and Stochastic Processes
Quadratic programming
Research Article
Simplex method
successive projection
system of linear inequalities
Topological Groups
system of linear inequalities
method of least squares
65K05
Householder transformation
90C05
Quadratic programming
successive projection
ISSN:1895-1074, 2391-5455, 1644-3616, 2391-5455
Online Access:Get full text
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Description
Summary: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.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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content type line 14
ISSN:1895-1074
2391-5455
1644-3616
2391-5455
DOI:10.2478/s11533-008-0012-1