ADDRESS DECLINE IN THE LEAST SQUARES PROBLEM OF A INTERIOR POINT METHOD FOR LINEAR PROGRAMMING
Keywords:Linear Programming, inner elipsoid, least square, descent direction
AbstractThis 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.
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.
How to Cite
The authors who publish in this journal accept the following conditions:
1. The authors retain the copyright and assign to the journal the right of the first publication, with the work registered with the Creative Commons Attribution License,Atribución 4.0 Internacional (CC BY 4.0) which allows third parties to use what is published whenever they mention the authorship of the work And to the first publication in this magazine.
2. Authors may make other independent and additional contractual arrangements for non-exclusive distribution of the version of the article published in this journal (eg, include it in an institutional repository or publish it in a book) provided they clearly state that The paper was first published in this journal.
3. Authors are encouraged to publish their work on the Internet (for example, on institutional or personal pages) before and during the review and publication process, as it can lead to productive exchanges and to a greater and more rapid dissemination Of the published work.