Papers
Refereed published, and submitted
- How do exponential size solutions arise in semidefinite programming? G. Pataki, A. Touzov
To appear, SIAM Journal on Optimization - A simplified treatment of Ramana’s exact dual for semidefinite programming B. Lourenco, G. Pataki,
Optimization Letters (2022): 1-25. - An echelon form of weakly infeasible semidefinite programs and bad projections of the psd cone G. Pataki, A. Touzov
Foundations of Computational Mathematics, 2022, 1–38. - On positive duality gaps in semidefinite programming G. Pataki
Submitted - Sieve-SDP: a simple facial reduction algorithm to preprocess semidefinite programs Y. Zhu, G. Pataki, Q. Tran-Dinh
Mathematical Programming Computation volume 11, pages 503–586, 2019 DOI - Characterizing bad semidefinite programs: normal forms and short proofs G. Pataki
SIAM Review 61(4), 839–859, 2019 DOI - Exact duals and short certificates of infeasibility and weak infeasibility in conic linear programming , M. Liu, G. Pataki,
Mathematical Programming, Ser. A 2018 167:435–480 DOI - Bad semidefinite programs: they all look the same G. Pataki
SIAM Journal on Optimization, 2017, 27(3), 146–172, 2017 DOI - Exact duality in semidefinite programming based on elementary reformulations , M. Liu, G. Pataki,
SIAM Journal on Optimization, 25(3), 1441–1454, 2015 DOI - Coordinate shadows of semi-definite and Euclidean distance matrices , D. Drusvyatsky, G. Pataki, H. Wolkowicz,
SIAM Journal on Optimization, 25(2), 1160–1178, 2015 DOI - Strong duality in conic linear programming: facial reduction and extended duals ,
Computational and Analytical Mathematics, Jonathan Borwein’s 60th birthday volume, 2013 - On the connection of facially exposed and nice cones G. Pataki,
Journal of Mathematical Analysis and Applications, Vol 400(1), April 2013, 211–221 DOI - 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) DOI - 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 DOI - Column Basis Reduction and Decomposable Knapsack Problems, B. Krishnamoorthy and G. Pataki,
Discrete Optimization, 6(3), August 2009, 242-270 DOI - On the Closedness of the Linear Image of a Closed Convex Cone , G. Pataki
Mathematics of Operations Research. 32(2), 395-412, 2007 DOI - Teaching Integer Programming Formulations Using the Traveling Salesman Problem, G. Pataki
SIAM Review, Vol 45, No. 1 (2003), 116-123 DOI - On the Generic Properties of Convex Optimization Problems in Conic Form, G. Pataki and L. Tuncel
Mathematical Programming, Series A 89 (2001) 449-457 - 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 - The Geometry of Semidefinite Programming G. Pataki,
In the The Handbook of Semidefinite Programming, Kluwer, 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 DOI - Cone-LP’s and Semidefinite Programs: Geometry and a Simplex-type Method, G. Pataki
1996 Conference on Integer Programming and Combinatorial Optimization (IPCO 5) - Schlumberger Optimizes Receiver Location for Automated Meter Reading, L. Clarke, S. Gavirneni and G. Pataki
Interfaces, Vol 34, No.3 (2004), 208-214 - Solving the seymour problem, M. C. Ferris, G. Pataki and S. Schmieta
Optima, 66:1-7, 2001. - Solving Integer and Disjunctive Programs by Lift-and-Project, S. Ceria and G. Pataki
1998 Conference on Integer Programming and Combinatorial Optimization (IPCO 6) - 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
Nonrefereed
- Book review of “In Pursuit of the Traveling Salesman”, G. Pataki
INFORMS Journal on Computing, Winter 2013.
Technical reports
- Unifying LLL inequalities G. Pataki and M. Tural
- A simple derivation of a facial reduction algorithm, and extended dual systems G. Pataki
Technical report, Columbia University, 2000 . This paper will remain a manuscript. However, its results are subsumed by the “Strong duality in conic linear programming…” paper