ADDRESS DECLINE IN THE LEAST SQUARES PROBLEM OF A INTERIOR POINT METHOD FOR LINEAR PROGRAMMING

Authors

  • Jenny Rojas Jerónimo
  • Carlos De la Cruz Chávez

DOI:

https://doi.org/10.17268/sel.mat.2015.02.07

Keywords:

Linear Programming, inner elipsoid, least square, descent direction

Abstract

This research work solves the problem of least squares that requires inner elipsoid algorithm to determine the descent direction; giving solution to linear programming problems by means of this method
of interior points. We solve the least squares problem using auxiliary function with logarithmic barrier and an approximation of the original matrix factorization by a matrix of rank one update to nally use the Sherman-Morrison-Woodburry formula and determining the inverse of the current matrix thus solving the least squares problem and obtaining a approximation to the descent direction.

References

Angel Salamanca Fernández, Jesús Juan Ruiz, Algoritmo del elipsoide interior para Programación Lineal, Questiió, 1991; 69-93.

Aeneas Marxen, Primal barrier methods for Linear Programming, Sol, 1989; 89-96.

C.T. Kelley, Iterative Methods for Linear and Nonlinear Equations, SIAM. 1998.

George B. Dantzig, Mukund N. Thapa, Linear Programming Introduction, 3era ed., Peter Glynn. 1997.

George B. Dantzig, Mukund N. Thapa, Linear Programming Theory and Extensions, 3era ed., Peter Glynn. 1997.

J.E. Dennis y Robert B. Schnabel, A View of Unconstrained Optimization. Operations Research and Management Science, 1988; 03-86.

Klee, V.Y, G.J. Minty, How good is the Simplex Algorithm? In Inequalities III. Shissha Ed Academic Press, New York, 1979; 159-175.

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Published

2015-12-28

How to Cite

Rojas Jerónimo, J., & De la Cruz Chávez, C. (2015). ADDRESS DECLINE IN THE LEAST SQUARES PROBLEM OF A INTERIOR POINT METHOD FOR LINEAR PROGRAMMING. Selecciones Matemáticas, 2(02), 129-145. https://doi.org/10.17268/sel.mat.2015.02.07

Issue

Vol. 2 No. 02 (2015): August - December

Section

Articles

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