Publications of Gabor Pataki
Convex Programming

Strong duality in conic linear programming: facial reduction and extended duals ,
Computational and Analytical Mathematics: proceedings of Jonfest, a conference in honor of Jonathan Borwein's 60th birthday
An earlier version appeared as: A Simple Derivation of a Facial Reduction Algorithm, and
Extended Dual Systems
Technical report, Columbia University, 2000

On the connection of facially exposed and nice cones ,
Journal of Mathematical Analysis and Applications, Vol 400(1), April 2013, 211221

Bad semidefinite programs: they all look the same ,
submitted

On the Closedness of the Linear Image of a Closed Convex Cone ,
Mathematics of Operations Research. Vol 32 (2), 395412, 2007
 The Geometry of Semidefinite Programming,
in H. Wolkowicz, L. Vandenberghe and R. Saigal, ed.: The Handbook of Semidefinite Programming, Kluwer, 2000

On the Generic Properties of Convex Optimization Problems in
Conic Form, G. Pataki and L. Tuncel
Mathematical Programming A 89 (2001) 449457
 On the Rank of Extreme Matrices in Semidefinite Programs and the
Multiplicity of Optimal Eigenvalues,
Mathematics of Operations Research, 23 (2), 339358, 1998
 ConeLP's and Semidefinite Programs: Geometry and
a Simplextype 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 BranchandBound, G. Pataki, M. Tural, E. B. Wong
2010 ACMSIAM 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, 242270
 Teaching Integer Programming Formulations Using the Traveling Salesman Problem,
SIAM Review, Vol 45, No. 1 (2003), 116123
 OCTANE: A New Heuristic for Pure 01 Programs, E. Balas, S. Ceria, M. Dawande, G. Pataki and F. Margot
Operations Research 49 (2001), 207235
 Solving Integer and Disjunctive Programs by LiftandProject, 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, 66:17, 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), 15971615
 Schlumberger Optimizes Receiver Location for Automated Meter
Reading, L. Clarke, S. Gavirneni and G. Pataki
Interfaces, Vol 34, No.3 (2004), 208214