Exact and stable least squares solution to the linear programming problem

• Autorzy: Evald Übi
• Języki publikacji: EN

Abstrakty

EN

A linear programming problem is transformed to the finding an element of polyhedron with the minimal norm. According to A. Cline [6], the problem is equivalent to the least squares problem on positive ortant. An orthogonal method for solving the problem is used. This method was presented earlier by the author and it is based on the highly developed least squares technique. First of all, the method is meant for solving unstable and degenerate problems. A new version of the artifical basis method (M-method) is presented. Also, the solving of linear inequality systems is considered.

Słowa kluczowe

EN

Linear programming; method of least squares; M-method; 90C05; 65K05

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2005
• Tom: 3
• Numer: 2
• Strony: 228-241

Daty

wydano

2005-06-01

online

2005-06-01

Twórcy

autor

Evald Übi

• Tallinn University of Technology

Bibliografia

• [1] E. Übi: “An Approximate Solution to Linear and Quadratic Programming Problems by the Method of least squares”, Proc. Estonian Acad. Sci. Phys. Math., Vol. 47, (1998), pp. 19–28.
• [2] E. Übi: “On Computing a Stable Least Squares Solution to the Linear Programming Problem”, Proc. Estonian Acad. Sci. Phys. Math., Vol 47, (1998), pp. 251–259.
• [3] E. Übi: “Finding Non-negative Solution of Overdetermined or Underdetermined System of Linear Equations by Method of Least Squares”, Trans. Tallinn Tech. Univ., Vol. 738, (1994), pp. 61–68.
• [4] R. Cline and R. Plemmons: l 2-solutions to Underdetermined Linear Systems SIAM Review, Vol. 10, (1976), pp. 92–105. http://dx.doi.org/10.1137/1018004
• [5] A. Cline: “An Elimination Method for the Solution of Linear Least Squares Problems”, SIAM J. Numer. Anal., Vol. 10, (1973), pp. 283–289. http://dx.doi.org/10.1137/0710027
• [6] C. Lawson and R. Hanson: Solving Least Squares Problems, Prentice-Hall, New-Jersey, 1974.
• [7] B. Poljak: Vvedenie v optimizatsiyu, Nauka, Moscow, 1983.
• [8] T. Hu: Integer programming and Network flows, Addison-Wesley Publishing Company, Massachusetts, 1970.

Identyfikatory

DOI

10.2478/BF02479198