-
1
-
-
0022145768
-
A simplex algorithm whose average number of steps is bounded between two quadratic functions of the smaller dimension
-
I. Adler and N. Megiddo, A simplex algorithm whose average number of steps is bounded between two quadratic functions of the smaller dimension, Journal of the Association of Computing Machinery 32 (1985) 891-895.
-
(1985)
Journal of the Association of Computing Machinery
, vol.32
, pp. 891-895
-
-
Adler, I.1
Megiddo, N.2
-
3
-
-
34249842390
-
A pivoting algorithm for convex hulls and vertex enumeration of arrangements and polyhedra
-
D. Avis and K. Fukuda, A pivoting algorithm for convex hulls and vertex enumeration of arrangements and polyhedra, Discrete and Computational Geometry 8 (1992) 295-313.
-
(1992)
Discrete and Computational Geometry
, vol.8
, pp. 295-313
-
-
Avis, D.1
Fukuda, K.2
-
6
-
-
0004196915
-
-
Cambridge University Press, Cambridge, MA
-
A. Björner, M. Las Vergnas, B. Sturmfels, N. White and G. Ziegler, Oriented Matroids (Cambridge University Press, Cambridge, MA, 1993).
-
(1993)
Oriented Matroids
-
-
Björner, A.1
Las Vergnas, M.2
Sturmfels, B.3
White, N.4
Ziegler, G.5
-
7
-
-
0000652462
-
New finite pivoting rules for the simplex method
-
R.G. Bland, New finite pivoting rules for the simplex method, Mathematics of Operations Research 2 (1977) 103-107.
-
(1977)
Mathematics of Operations Research
, vol.2
, pp. 103-107
-
-
Bland, R.G.1
-
8
-
-
0012910206
-
A combinatorial abstraction of linear programming
-
R.G. Bland, A combinatorial abstraction of linear programming, Journal of Combinatorial Theory, Series B 23 (1977) 33-57.
-
(1977)
Journal of Combinatorial Theory, Series B
, vol.23
, pp. 33-57
-
-
Bland, R.G.1
-
12
-
-
0040816989
-
-
Technical Report 79-14, Department of Operations Research, Stanford University, Stanford, CA
-
Y.Y. Chang, Least index resolution of degeneracy in linear complementarity problems, Technical Report 79-14, Department of Operations Research, Stanford University, Stanford, CA, 1979.
-
(1979)
Least Index Resolution of Degeneracy in Linear Complementarity Problems
-
-
Chang, Y.Y.1
-
13
-
-
0000014724
-
Optimality and degeneracy in linear programming
-
A. Charnes, Optimality and degeneracy in linear programming, Econometrica 20 (1952) 160-170.
-
(1952)
Econometrica
, vol.20
, pp. 160-170
-
-
Charnes, A.1
-
15
-
-
0004139889
-
-
W.H. Freeman and Company, San Francisco
-
V. Chvátal, Linear Programming (W.H. Freeman and Company, San Francisco, 1983).
-
(1983)
Linear Programming
-
-
Chvátal, V.1
-
16
-
-
0023365765
-
A note on Edmonds-Fukuda pivoting rule for the simplex method
-
J. Clausen, A note on Edmonds-Fukuda pivoting rule for the simplex method, European Journal of Operations Research 29 (1987) 378-383.
-
(1987)
European Journal of Operations Research
, vol.29
, pp. 378-383
-
-
Clausen, J.1
-
21
-
-
0003770439
-
Programming in a linear structure
-
USAF Washington, DC February
-
G.B. Dantzig, Programming in a linear structure, Comptroller, USAF Washington, DC (February 1948).
-
(1948)
Comptroller
-
-
Dantzig, G.B.1
-
23
-
-
0002120628
-
Linear programming: The story about how it began
-
A.H.G. Rinnoy Kan, L.K. Lenstra and A. Schrijver, eds., CWI, North-Holland, Amsterdam
-
G.B. Dantzig, Linear programming: The story about how it began, in: A.H.G. Rinnoy Kan, L.K. Lenstra and A. Schrijver, eds., History of Mathematical Programming (CWI, North-Holland, Amsterdam, 1991) 19-31.
-
(1991)
History of Mathematical Programming
, pp. 19-31
-
-
Dantzig, G.B.1
-
24
-
-
84972521846
-
The generalized simplex method for minimizing a linear form under linear inequality restraints
-
G.B. Dantzig, A. Orden and P. Wolfe, The generalized simplex method for minimizing a linear form under linear inequality restraints, Pacific Journal of Mathematics 5 (1955) 183-195.
-
(1955)
Pacific Journal of Mathematics
, vol.5
, pp. 183-195
-
-
Dantzig, G.B.1
Orden, A.2
Wolfe, P.3
-
29
-
-
0004144178
-
-
Ph.D. Thesis, Waterloo University, Waterloo, Ontario, Canada
-
K. Fukuda, Oriented matroid programming, Ph.D. Thesis, Waterloo University, Waterloo, Ontario, Canada, 1982.
-
(1982)
Oriented Matroid Programming
-
-
Fukuda, K.1
-
31
-
-
30244571999
-
Combinatorial maximum improvement algorithm for LP and LCP
-
Brest, France
-
K. Fukuda and H.-J. Lüthi, Combinatorial maximum improvement algorithm for LP and LCP, Presented at Franco-Japanese Days, Brest, France, 1995.
-
(1995)
Franco-Japanese Days
-
-
Fukuda, K.1
Lüthi, H.-J.2
-
33
-
-
0028426087
-
On extremal behaviors of Murty's least index method
-
K. Fukuda and M. Namiki, On extremal behaviors of Murty's least index method, Mathematical Programming 64 (1994) 365-370.
-
(1994)
Mathematical Programming
, vol.64
, pp. 365-370
-
-
Fukuda, K.1
Namiki, M.2
-
34
-
-
30244525816
-
Finding all common basis in two matroids
-
K. Fukuda and M. Namiki, Finding all common basis in two matroids, Discrete Applied Mathematics 56 (1995) 231-243.
-
(1995)
Discrete Applied Mathematics
, vol.56
, pp. 231-243
-
-
Fukuda, K.1
Namiki, M.2
-
35
-
-
30244494306
-
-
Technical Report, Institute for Operations Research, ETH-Zentrum, CH-8092 Zürich, Switzerland
-
K. Fukuda, M. Namiki and A. Tamura, EP theorems and linear complementarity problems, Technical Report, Institute for Operations Research, ETH-Zentrum, CH-8092 Zürich, Switzerland, 1996.
-
(1996)
EP Theorems and Linear Complementarity Problems
-
-
Fukuda, K.1
Namiki, M.2
Tamura, A.3
-
37
-
-
0003881812
-
-
Technical Report, Department of Industrial Engineering and Operations Research, Columbia University
-
D. Goldfarb, Worst case complexity of the shadow vertex simplex algorithm, Technical Report, Department of Industrial Engineering and Operations Research, Columbia University, 1983.
-
(1983)
Worst Case Complexity of the Shadow Vertex Simplex Algorithm
-
-
Goldfarb, D.1
-
38
-
-
21144476593
-
The linear complementarity problem, sufficient matrices and the criss-cross method
-
D. Den Hertog, C. Roos and T. Terlaky, The linear complementarity problem, sufficient matrices and the criss-cross method, Linear Algebra and Its Applications 187 (1993) 1-14.
-
(1993)
Linear Algebra and its Applications
, vol.187
, pp. 1-14
-
-
Den Hertog, D.1
Roos, C.2
Terlaky, T.3
-
39
-
-
30244521963
-
-
Report No. 96-103, Faculteit der Technische Wiskunde en Informatica, Technische Universiteit Delft, The Netherlands
-
T. Illés, Á. Szirmai and T. Terlaky, A finite criss-Cross method for hyperbolic programming, Report No. 96-103, Faculteit der Technische Wiskunde en Informatica, Technische Universiteit Delft, The Netherlands, 1996; also in: European Journal of Operations Research, to appear.
-
(1996)
A Finite Criss-cross Method for Hyperbolic Programming
-
-
Illés, T.1
Szirmai, Á.2
Terlaky, T.3
-
40
-
-
30244486955
-
-
to appear
-
T. Illés, Á. Szirmai and T. Terlaky, A finite criss-Cross method for hyperbolic programming, Report No. 96-103, Faculteit der Technische Wiskunde en Informatica, Technische Universiteit Delft, The Netherlands, 1996; also in: European Journal of Operations Research, to appear.
-
European Journal of Operations Research
-
-
-
41
-
-
0345302264
-
-
Ph.D. Thesis, School of OR and IE, Cornell University, Ithaca, NY
-
D. Jensen, Coloring and duality: Combinatorial augmentation methods, Ph.D. Thesis, School of OR and IE, Cornell University, Ithaca, NY, 1985.
-
(1985)
Coloring and Duality: Combinatorial Augmentation Methods
-
-
Jensen, D.1
-
42
-
-
84967739006
-
A quasi-polynomial bound for the diameter of graphs of polyhedra
-
G. Kalai and D. Kleitman, A quasi-polynomial bound for the diameter of graphs of polyhedra, Bull. Amer. Math. Soc. 26 (1992) 315-316.
-
(1992)
Bull. Amer. Math. Soc.
, vol.26
, pp. 315-316
-
-
Kalai, G.1
Kleitman, D.2
-
43
-
-
51249181779
-
A new polynomial-time algorithm for linear programming
-
N. Karmarkar, A new polynomial-time algorithm for linear programming, Combinatorica 4 (1984) 373-395.
-
(1984)
Combinatorica
, vol.4
, pp. 373-395
-
-
Karmarkar, N.1
-
44
-
-
0001000105
-
Polynomial algorithms in linear programming
-
in Russian
-
L.G. Khachian, Polynomial algorithms in linear programming, Zhurnal Vichislitelnoj Matematiki i Matematischeskoi Fiziki 20 (1980) 51-68 (in Russian); English translation in: USSR Computational Mathematics and Mathematical Physics 20 (1980) 53-72.
-
(1980)
Zhurnal Vichislitelnoj Matematiki i Matematischeskoi Fiziki
, vol.20
, pp. 51-68
-
-
Khachian, L.G.1
-
45
-
-
0011260909
-
-
English translation in
-
L.G. Khachian, Polynomial algorithms in linear programming, Zhurnal Vichislitelnoj Matematiki i Matematischeskoi Fiziki 20 (1980) 51-68 (in Russian); English translation in: USSR Computational Mathematics and Mathematical Physics 20 (1980) 53-72.
-
(1980)
USSR Computational Mathematics and Mathematical Physics
, vol.20
, pp. 53-72
-
-
-
46
-
-
0007808985
-
Some generalizations of the criss-cross method for quadratic programming
-
E. Klafszky and T. Terlaky, Some generalizations of the criss-cross method for quadratic programming, Math. Oper. und Stat. Ser. Optimization 24 (1992) 127-139.
-
(1992)
Math. Oper. und Stat. Ser. Optimization
, vol.24
, pp. 127-139
-
-
Klafszky, E.1
Terlaky, T.2
-
47
-
-
25444479797
-
Some generalizations of the criss-cross method for the linear complementarity problem of oriented matroids
-
E. Klafszky and T. Terlaky, Some generalizations of the criss-cross method for the linear complementarity problem of oriented matroids, Combinatorica 9 (1989) 189-198.
-
(1989)
Combinatorica
, vol.9
, pp. 189-198
-
-
Klafszky, E.1
Terlaky, T.2
-
48
-
-
0001849163
-
How good is the simplex algorithm?
-
O. Shisha, ed., Academic Press, New York
-
V. Klee and G.J. Minty, How good is the simplex algorithm? in: O. Shisha, ed., Inequalities - III (Academic Press, New York, 1972) 159-175.
-
(1972)
Inequalities - III
, pp. 159-175
-
-
Klee, V.1
Minty, G.J.2
-
50
-
-
0003212154
-
A unified approach to interior point algorithms for linear complementarity problems
-
Springer, Berlin
-
M. Kojima, N. Megiddo, T. Noma and A. Yoshise, A Unified Approach to Interior Point Algorithms for Linear Complementarity Problems, Lecture Notes in Computer Science, Vol. 538 (Springer, Berlin, 1991).
-
(1991)
Lecture Notes in Computer Science
, vol.538
-
-
Kojima, M.1
Megiddo, N.2
Noma, T.3
Yoshise, A.4
-
51
-
-
0000176346
-
Equilibrium points of bimatrix games
-
C.E. Lemke and J.T. Howson Jr, Equilibrium points of bimatrix games, SIAM Journal 12 (1964) 413-423.
-
(1964)
SIAM Journal
, vol.12
, pp. 413-423
-
-
Lemke, C.E.1
Howson J.T., Jr.2
-
52
-
-
0002352416
-
On complementary pivot theory
-
G.B. Dantzig and A.F. Veinott, eds., AMS, Providence, RI
-
C.E. Lemke, On complementary pivot theory, in: G.B. Dantzig and A.F. Veinott, eds., Mathematics of Decision Sciences, Part 1 (AMS, Providence, RI, 1968) 95-114.
-
(1968)
Mathematics of Decision Sciences
, Issue.1 PART
, pp. 95-114
-
-
Lemke, C.E.1
-
53
-
-
0041548663
-
On the number of iterations of the simplex method
-
R. Henn, H.P. Künzi and H. Schubert, eds., Verlag Anton
-
T.M. Liebling, On the number of iterations of the simplex method, in: R. Henn, H.P. Künzi and H. Schubert, eds., Methods of Operations Research XVII (Verlag Anton, 1972) 248-264.
-
(1972)
Methods of Operations Research
, vol.17
, pp. 248-264
-
-
Liebling, T.M.1
-
54
-
-
30244563893
-
-
Technical Report SOL 87-4, Department of Operations Research, Stanford University, Stanford, California
-
I. Lustig, The equivalence of Dantzig's self-dual parametric algorithm for linear programs to Lemke's algorithm for linear complementarity problems applied to linear programming, Technical Report SOL 87-4, Department of Operations Research, Stanford University, Stanford, California, 1987.
-
(1987)
The Equivalence of Dantzig's Self-dual Parametric Algorithm for Linear Programs to Lemke's Algorithm for Linear Complementarity Problems Applied to Linear Programming
-
-
Lustig, I.1
-
55
-
-
0004122788
-
-
Ph.D. Thesis, Waterloo University, Waterloo, Ontario
-
A. Mandel, Topology of oriented matroids, Ph.D. Thesis, Waterloo University, Waterloo, Ontario, 1982.
-
(1982)
Topology of Oriented Matroids
-
-
Mandel, A.1
-
56
-
-
30244504072
-
-
Technical Report No. 631, Cornell University, School of Operations Research and Industrial Engineering, Ithaca, NY
-
W. Morris Jr and M.J. Todd, Symmetry and positive definiteness in oriented matroids, Technical Report No. 631, Cornell University, School of Operations Research and Industrial Engineering, Ithaca, NY, 1984.
-
(1984)
Symmetry and Positive Definiteness in Oriented Matroids
-
-
Morris W., Jr.1
Todd, M.J.2
-
57
-
-
0000019570
-
A note on a Bard type scheme for solving the complementarity problem
-
K.G. Murty, A note on a Bard type scheme for solving the complementarity problem, Opsearch 11 (2-3) (1974) 123-130.
-
(1974)
Opsearch
, vol.11
, Issue.2-3
, pp. 123-130
-
-
Murty, K.G.1
-
59
-
-
0000649264
-
Computational complexity of parametric linear programming
-
K.G. Murty, Computational complexity of parametric linear programming, Mathematical Programming 19 (1980) 213-219.
-
(1980)
Mathematical Programming
, vol.19
, pp. 213-219
-
-
Murty, K.G.1
-
60
-
-
10944233591
-
-
Research Report, Department of Information Sciences, Tokyo Institute of Technology, Tokyo
-
M. Namiki and T. Matsui, Some modifications of the criss-cross method, Research Report, Department of Information Sciences, Tokyo Institute of Technology, Tokyo, 1990.
-
(1990)
Some Modifications of the Criss-cross Method
-
-
Namiki, M.1
Matsui, T.2
-
61
-
-
0012742221
-
Pivoting rules directing the simplex method through all feasible vertices of Klee-Minty examples
-
K. Paparrizos, Pivoting rules directing the simplex method through all feasible vertices of Klee-Minty examples, Opsearch 26 (2) (1989) 77-95.
-
(1989)
Opsearch
, vol.26
, Issue.2
, pp. 77-95
-
-
Paparrizos, K.1
-
62
-
-
0025235586
-
An exponential example for Terlaky's pivoting rule for the criss-cross simplex method
-
C. Roos, An exponential example for Terlaky's pivoting rule for the criss-cross simplex method, Mathematical Programming 46 (1990) 78-94.
-
(1990)
Mathematical Programming
, vol.46
, pp. 78-94
-
-
Roos, C.1
-
65
-
-
0040321298
-
Egy új, véges criss-cross módszer lineáris programozási feladatok megoldására
-
T. Terlaky, Egy új, véges criss-cross módszer lineáris programozási feladatok megoldására, Alkalmazott Matematikai Lapok 10 (1984) 289-296 (in Hungarian, English title: A new, finite criss-cross method for solving linear programming problems).
-
(1984)
Alkalmazott Matematikai Lapok
, vol.10
, pp. 289-296
-
-
Terlaky, T.1
-
68
-
-
0040915269
-
A finite criss-cross method for oriented matroids
-
T. Terlaky, A finite criss-cross method for oriented matroids, Journal of Combinatorial Theory, Series B 42 (3) (1987) 319-327.
-
(1987)
Journal of Combinatorial Theory, Series B
, vol.42
, Issue.3
, pp. 319-327
-
-
Terlaky, T.1
-
70
-
-
0344271280
-
Pivot rules for linear programming: A survey on recent theoretical developments
-
T. Terlaky and S. Zhang, Pivot rules for linear programming: A survey on recent theoretical developments, Annals of Operations Research 46 (1993) 203-233.
-
(1993)
Annals of Operations Research
, vol.46
, pp. 203-233
-
-
Terlaky, T.1
Zhang, S.2
-
72
-
-
0042926851
-
Linear and quadratic programming in oriented matroids
-
M.J. Todd, Linear and quadratic programming in oriented matroids, Journal of Combinatorial Theory, Series B 39 (1985) 105-133.
-
(1985)
Journal of Combinatorial Theory, Series B
, vol.39
, pp. 105-133
-
-
Todd, M.J.1
-
73
-
-
0022739464
-
Polynomial expected behavior of a pivoting algorithm for linear complementarity and linear programming problems
-
M.J. Todd, Polynomial expected behavior of a pivoting algorithm for linear complementarity and linear programming problems, Mathematical Programming 35 (1986) 173-192.
-
(1986)
Mathematical Programming
, vol.35
, pp. 173-192
-
-
Todd, M.J.1
-
74
-
-
30244439941
-
A note on convergence of the Ford-Fulkerson flow algorithm
-
A. Tucker, A note on convergence of the Ford-Fulkerson flow algorithm, Mathematics of Operations Research 2 (2) (1977) 143-144.
-
(1977)
Mathematics of Operations Research
, vol.2
, Issue.2
, pp. 143-144
-
-
Tucker, A.1
-
75
-
-
84859267215
-
A new proof of the finiteness of the criss-cross method
-
H. Väliaho, A new proof of the finiteness of the criss-cross method, Math. Oper. und Stat. ser. Optimization 25 (1992) 391-400.
-
(1992)
Math. Oper. und Stat. Ser. Optimization
, vol.25
, pp. 391-400
-
-
Väliaho, H.1
-
77
-
-
0040321297
-
A conformal elimination free algorithm for oriented matroid programming
-
Zh. Wang, A conformal elimination free algorithm for oriented matroid programming, Chinese Annals of Mathematics 8 (B1) (1987).
-
(1987)
Chinese Annals of Mathematics
, vol.8
, Issue.B1
-
-
Wang, Zh.1
-
78
-
-
84903638103
-
A modified version of the Edmonds-Fukuda algorithm for LP in the general form
-
Zh. Wang, A modified version of the Edmonds-Fukuda algorithm for LP in the general form, Asia-Pacific Journal of Operations Research 8 (1) (1991).
-
(1991)
Asia-Pacific Journal of Operations Research
, vol.8
, Issue.1
-
-
Wang, Zh.1
-
79
-
-
30244548722
-
A general deterministic pivot method for oriented matroid programming
-
Zh. Wang, A general deterministic pivot method for oriented matroid programming, Chinese Annals of Mathematics B 13 (2) (1992).
-
(1992)
Chinese Annals of Mathematics B
, vol.13
, Issue.2
-
-
Wang, Zh.1
-
80
-
-
25444504609
-
A general scheme for solving linear complementarity problems in the setting of oriented matroids
-
H.P. Yap, T.H. Ku, E.K. Lloyd and Zh. Wang, eds., China World Scientific, Singapore
-
Zh. Wang and T. Terlaky, A general scheme for solving linear complementarity problems in the setting of oriented matroids, in: H.P. Yap, T.H. Ku, E.K. Lloyd and Zh. Wang, eds., Combinatorics and Graph Theory, Proceedings of the Spring School and International Conference on Combinatorics: SSIC'92, China (World Scientific, Singapore, 1993) 244-255.
-
(1993)
Combinatorics and Graph Theory, Proceedings of the Spring School and International Conference on Combinatorics: SSIC'92
, pp. 244-255
-
-
Wang, Zh.1
Terlaky, T.2
-
82
-
-
0003647332
-
-
Technical Report No. 27, Department of Operations Research, Stanford University, Stanford, CA
-
N. Zadeh, What is the worst case behavior of the simplex algorithm? Technical Report No. 27, Department of Operations Research, Stanford University, Stanford, CA, 1980.
-
(1980)
What Is the Worst Case Behavior of the Simplex Algorithm?
-
-
Zadeh, N.1
-
83
-
-
0042708132
-
On anti-cycling pivoting rules for the simplex method
-
S. Zhang, On anti-cycling pivoting rules for the simplex method, Operations Research Letters 10 (1991) 189-192.
-
(1991)
Operations Research Letters
, vol.10
, pp. 189-192
-
-
Zhang, S.1
-
84
-
-
30244437053
-
-
Technical Report, Econometric Institute, Erasmus University Rotterdam, 9707/A
-
S. Zhang, New variants of finite criss-cross pivot algorithms for linear programming, Technical Report, Econometric Institute, Erasmus University Rotterdam, 9707/A, 1997.
-
(1997)
New Variants of Finite Criss-cross Pivot Algorithms for Linear Programming
-
-
Zhang, S.1
-
85
-
-
0001123164
-
The criss-cross method for solving linear programming problems
-
S. Zionts, The criss-cross method for solving linear programming problems, Management Science 15 (7) (1969) 426-445.
-
(1969)
Management Science
, vol.15
, Issue.7
, pp. 426-445
-
-
Zionts, S.1
-
86
-
-
30244538317
-
Some empirical test of the criss-cross method
-
S. Zionts, Some empirical test of the criss-cross method, Management Science 19 (1972) 406-410.
-
(1972)
Management Science
, vol.19
, pp. 406-410
-
-
Zionts, S.1
|