zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
A note on “An improved initial basis for the simplex algorithm”. (English) Zbl 1165.90566
Summary: We show a mathematical error in the paper “An improved initial basis for the simplex algorithm” [{\it H. Vieira Junior} and {M. Pereira Estellita Lins}, Comput. Oper. Res. 32, No. 8, 1983--1993 (2005; Zbl 1068.90079)], and then offer a modified method using LU decomposition. Our preliminary computational results are very favorable.

90C05Linear programming
90C49Extreme-point and pivoting methods
Full Text: DOI
[1] Stojkovic, N. V.; Stanimirovic, P. S.: Two direct methods in linear programming. European journal of operational research 131, 417-439 (2001)
[2] Trigos, F.; Lopez, R. R. Frausto-Solis: A simplex cosine method for solving the klee-minty cube. Advances in simulation system theory and systems engineering 70X, 27-32 (2002)
[3] Junior, H. V.; Lins, M. P. E.: An improved initial basis for the simplex algorithm. Computers and operations research. 32, 1983-1993 (2005) · Zbl 1068.90079
[4] Corley HW, Rosenberger J, Yeh W-C, Sung TK. The cosine simplex algorithm. The International Journal of Advanced Manufacturing Technology 2005; 27:1047 -- 50.
[5] Pan, P. -Q.: Practical finite pivoting rules for the simplex method. OR spektrum 12, 219-225 (1990) · Zbl 0714.90063
[6] Fei H-y. A crash simplex method for linear programming based on the characterization of the optimal solution. Master degree thesis, Southeast University, China; 2000.
[7] Pan, P. -Q.: Primal perturbation simplex algorithms for linear programming. Journal of computational mathematics 18, No. 6, 587-596 (2000) · Zbl 0985.65064