A numerically stable least squares solution to the quadratic programming problem

• Autorzy: E. Übi
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Quadratic programming; system of linear inequalities; method of least squares; Householder transformation; successive projection

Kategorie tematyczne

• 65K05: Mathematical programming methods
• 90C05: Linear programming

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2008
• Tom: 6
• Numer: 1
• Strony: 171-178

Daty

wydano

2008-03-01

online

2008-02-26

Twórcy

autor

E. Übi

• Tallinn University of Technology

Bibliografia

• [1] Goldfarb D., Idnani A., A Numerically stable dual method for solving strictly convex quadratic programs, Math. Programming, 1983, 27, 1–33 http://dx.doi.org/10.1007/BF02591962
• [2] Künzi H.P., Krelle W., Nichtlineare Programmirung, Springer, Berlin, 1962 (in German)
• [3] Lawson C.L., Hanson R.J., Solving least squares problems, Prentice-Hall, New-Jersey, 1974
• [4] Lent A., Censor Y., Extensions of Hildreth’s row action method for quadratic programming, SIAM J. Control Optim., 1980, 18, 444–454 http://dx.doi.org/10.1137/0318033
• [5] Powell M.J.D., On the quadratic programming algorithm of Goldfarb and Idnani, Math. Programming Stud., 1985, 25, 46–61
• [6] Übi E., On stable least squares solution to the system of linear inequalities, Cent. Eur. J. Math., 2007, 5, 373–385 http://dx.doi.org/10.2478/s11533-007-0003-7
• [7] Übi E., Exact and stable least squares solution to the linear programming problem, Cent. Eur. J. Math., 2005, 3, 228–241 http://dx.doi.org/10.2478/BF02479198

Identyfikatory

DOI

10.2478/s11533-008-0012-1