Criss-Cross Methods: A Fresh View on Pivot Algorithms

Criss-Cross Methods: A Fresh View on Pivot Algorithms (1997)

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by Komei Fukuda , Tamás Terlaky

Venue:	Mathematical Programming
Citations:	14 - 4 self

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@INPROCEEDINGS{Fukuda97criss-crossmethods:,
    author = {Komei Fukuda and Tamás Terlaky},
    title = {Criss-Cross Methods: A Fresh View on Pivot Algorithms},
    booktitle = {Mathematical Programming},
    year = {1997},
    pages = {369--395}
}

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Abstract

this paper is to present mathematical ideas and

Citations

638	Linear Programming and Extensions - Dantzig - 1963
539	A new polynomial-time algorithm for linear programming - Karmarkar - 1984
446	The Linear Complementarity Problem - Cottle, Pang, et al. - 1992
146	K: A pivoting algorithm for convex hulls and vertex enumeration of arrangements and polyhedra. Discrete Comput Geom - Avis, Fukuda - 1992
138	How good is the simplex algorithm - Klee, Minty - 1969
131	A Unified Approach to Interior Point Algorithms for Linear Complimentarity Problems - Kojima, Meggido, et al. - 1991
100	A polynomial algorithm for linear programming - Khachian - 1979
54	Oriented matroids - Folkman, Lawrence - 1978
52	Complementary pivot theory of mathematical programming - Cottle, Dantzig - 1968
42	The Simplex Method: A Probabilistic Analysis, volume 1 of Algorithms and Combinatorics - Borgwardt - 1987
42	The d-step conjecture and its relatives - Klee, Kleinschmidt - 1987
41	Las Vergnas, Orientability of Matroids - Bland, M - 1978
40	Kleitman D.: A quasi-polynomial bound for the diameter of graphs of polyhedra - Kalai - 1992
37	New finite pivoting rules for the simplex method - Bland - 1977
29	A simplex algorithm whose average number of steps is bounded between two quadratic functions of the smaller dimension - Adler, Megiddo - 1985
28	The diameter of graphs of convex polytopes and f-vector theory. In Applied geometry and discrete mathematics - Kalai - 1991
24	The generalized simplex method for minimizing a linear form under linear inequality restraints - Dantzig, Orden, et al. - 1955
21	Oriented matroid programming - Fukuda - 1982
17	A combinatorial abstraction of linear programming - Bland - 1977
17	Programming in a linear structure - Dantzig - 1948
16	Sufficient matrices and the linear complementarity problem. Linear Algebra and its Applications 114/115 - Cottle, Pang, et al. - 1989
13	Some generalizations of the criss-cross method for quadratic programming - Klafszky, Terlaky - 1992
12	Linear complementarity and oriented matroids - Fukuda, Terlaky - 1992
12	Worst case complexity of the shadow vertex simplex algorithm - Goldfarb - 1983
9	Existentially polytime theorems - Cameron, Edmonds - 1990
9	Some Generalizations of the Criss--Cross Method for the Linear Complementarity Problem of Oriented Matroids - Klafszky, Terlaky - 1989
8	Least index resolution of degeneracy in linear complementarity problems - Chang - 1979
8	The existence of a short sequence of admissible pivots to an optimal basis - Fukuda, Lüthi, et al. - 1997
7	The linear complementarity problem, sufficient matrices and the criss-cross method. Linear Algebra and Its Applications - Hertog, Roos, et al. - 1993
6	Linear Programming: The Story About How It Began - Dantzig - 1991
6	On the Finiteness of the Criss-Cross Method - Fukuda, Matsui
6	Colouring and Duality: Combinatorial Augmentation Methods - Jensen - 1985
5	Ep theorems and linear complementarity problems. Discrete Applied Mathematics - Fukuda, Namiki, et al. - 1998
5	The role of pivoting in proving some fundamental theorems of linear algebra, Linear Algebra Applications 151 - Klafszky, Terlaky - 1991
4	On extremal behaviors of Murty's least index method - Fukuda, Namiki - 1994
3	A Note on Edmonds-Fukuda Pivoting Rule for the Simplex Method - Clausen - 1987
3	The simplex method is very good! - on the expected number of pivot steps and related properties of random linear programs, Report - Haimovitz - 1983
2	The simplex method: it keeps getting better - Bixby - 1991
2	Optimality and degeneracy in linear programming, Econometrica 20(1952)160--170 - Charnes - 1952
2	The simplex algorithm with a new primal and dual pivot rule - Chen, Pardalos, et al. - 1994
2	A finite Criss-Cross Method for Hyperbolic Programming, Report No. 96--103, Faculteit der Technische Wiskunde en - Szirmai, Terlaky - 1996
1	Symmetric dual quadratic programs, Quart - Cottle - 1963
1	Exact pivoting, presentation - Edmonds - 1994
1	A Helly method for linear programming - Edmonds - 1994
1	NP easy and LP theory, Cours postgrade en Recherche Op'erationnelle, ' Ecole Polytechnique F'ed'erale de - Edmonds, Fukuda - 1994
1	The existence of a short sequence of admissible pivots - Fukuda, Luthi, et al.
1	Combinatorial maximum improvement algorithm for LP and LCP, presented at Franco-Japanese Days - Fukuda, Luthi - 1995
1	Finding all common basis in two matroids, Discrete Applied Mathematics 56 - Fukuda, Namiki - 1995