Publications of Gabor Pataki
Convex Programming
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Bad semidefinite programs: they all look the same ,
G. Pataki
submitted
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On the Closedness of the Linear Image of a Closed Convex Cone ,
G. Pataki
Mathematics of Operations Research. Vol 32 (2), 395-412, 2007
- The Geometry of Cone-LP's,
G. Pataki,
in H. Wolkowicz, L. Vandenberghe and R. Saigal, ed.: The Handbook of Semidefinite Programming, Kluwer, 2000
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On the Generic Properties of Convex Optimization Problems in
Conic Form,
G. Pataki and L. Tuncel
Mathematical Programming A 89 (2001) 449-457
- A Simple Derivation of a Facial Reduction Algorithm, and
Extended Dual Systems
G. Pataki
Technical report, Columbia University, 2000
- On the Rank of Extreme Matrices in Semidefinite Programs and the
Multiplicity of Optimal Eigenvalues,
G. Pataki
Mathematics of Operations Research, 23 (2), 339-358, 1998
- Cone-LP's and Semidefinite Programs: Geometry and
a Simplex-type Method,
G. Pataki
1996 Conference on Integer Programming and Combinatorial Optimization (IPCO 5)
Integer Programming
- Basis Reduction Methods (A survey of Lenstra's algorithm, Kannan's algorithm, and lattice based reformulation methods)
G. Pataki and M. Tural
Wiley Encyclopaedia of Operations Research and Management Science, 2011
- Basis Reduction, and the Complexity of Branch-and-Bound,
G. Pataki, M. Tural, E. B. Wong
2010 ACM-SIAM Symposium on Discrete Algorithms (SODA 10)
- Branching proofs of infeasibility in low density subset sum problems,
G. Pataki and M. Tural,
submitted
- Unifying LLL inequalities
G. Pataki and M. Tural,
submitted
- LLL Reduction, and the Parallel Approximation Problem,
G. Pataki and M. Tural,
Proceedings of the LLL+25 conference
Note: the results of this paper are subsumed by the above 2 papers.
- Column Basis Reduction and Decomposable Knapsack Problems,
B. Krishnamoorthy and G. Pataki,
Discrete Optimization, 6(3), August 2009, 242-270
- Teaching Integer Programming Formulations Using the Traveling Salesman Problem,
G. Pataki
SIAM Review, Vol 45, No. 1 (2003), 116-123
- OCTANE: A New Heuristic for Pure 0-1 Programs,
E. Balas, S. Ceria, M. Dawande, G. Pataki and F. Margot
Operations Research 49 (2001), 207-235
- Solving Integer and Disjunctive Programs by Lift-and-Project,
S. Ceria and G. Pataki
1998 Conference on Integer Programming and Combinatorial Optimization (IPCO 6)
- Solving the seymour problem,
M. C. Ferris, G. Pataki and S. Schmieta
Optima, 66:1-7, 2001.
- Polyhedral Methods for the Maximum Clique Problem,
E. Balas, S. Ceria, G. Cornuejols and G. Pataki
Second DIMACS Implementation Challenge: Maximum Clique, Graph Coloring, and Satisfiability 1996
Applications of Optimization
- A Principal Component Analysis for Trees
B. Aydin, G. Pataki, H. Wang, E. Bullitt, and S. Marron,
Annals of Applied Statistics, Volume 3, Number 4 (2009), 1597-1615
- Schlumberger Optimizes Receiver Location for Automated Meter
Reading,
L. Clarke, S. Gavirneni and G. Pataki
Interfaces, Vol 34, No.3 (2004), 208-214