International Research journal of Management Science and Technology

  ISSN 2250 - 1959 (online) ISSN 2348 - 9367 (Print) New DOI : 10.32804/IRJMST

Impact Factor* - 6.2311


**Need Help in Content editing, Data Analysis.

Research Gateway

Adv For Editing Content

   No of Download : 57    Submit Your Rating     Cite This   Download        Certificate

RANDOMIZED PERFECTION BY SIMPLEX METHOD

    1 Author(s):  SHINDE JAYESH SATISH

Vol -  6, Issue- 10 ,         Page(s) : 232 - 236  (2015 ) DOI : https://doi.org/10.32804/IRJMST

Abstract

In mathematical optimization, Dantzig's simplex algorithm (or simplex method) is a popular algorithm for linear programming.The journal Computing in Science and Engineering listed it as one of the top 10 algorithms of the twentieth century. The name of the algorithm is derived from the concept of a simplex and was suggested by T. S. Motzkin. Simplices are not actually used in the method, but one interpretation of it is that it operates on simplicial cones, and these become proper simplices with an additional constraint.The simplicial cones in question are the corners (i.e., the neighborhoods of the vertices) of a geometric object called a polytope. The shape of this polytope is defined by the constraints applied to the objective function.

1. Dmitris Alevras and Manfred W. Padberg, Linear Optimization and Extensions: Problems and Extensions, Universitext, Springer-Verlag, 2001. (Problems from Padberg with solutions.)
2. Maros, István; Mitra, Gautam (1996). "Simplex algorithms". In J. E. Beasley. Advances in linear and integer programming. Oxford Science. pp. 1–46. MR 1438309.
3. Maros, István (2003). Computational techniques of the simplex method. International Series in Operations Research & Management Science 61. Boston, MA: Kluwer Academic Publishers. pp. xx+325. ISBN 1-4020-7332-1. MR 1960274.
4. Bland, Robert G. (May 1977). "New finite pivoting rules for the simplex method". Mathematics of Operations Research 2 (2): 103–107. doi:10.1287/moor.2.2.103. JSTOR 3689647. MR 459599.
5. There are abstract optimization problems, called oriented matroid programs, on which Bland's rule cycles (incorrectly) while the criss-cross algorithm terminates correctly.
6. Klee, Victor; Minty, George J. (1972). "How good is the simplex algorithm?". In Shisha, Oved. Inequalities III (Proceedings of the Third Symposium on Inequalities held at the University of California, Los Angeles, Calif., September 1–9, 1969, dedicated to the memory of Theodore S. Motzkin). New York-London: Academic Press. pp. 159–175. MR 332165.

*Contents are provided by Authors of articles. Please contact us if you having any query.






Bank Details