Papers

Refereed published, and submitted

• An echelon form of weakly infeasible semidefinite programs and bad projections of the psd cone   G. Pataki, A. Touzov
  Foundations of Computational Mathematics, to appear
  Talk at the Fields Institute, by Alex Touzov, May 11, 2021   with a slightly different title.
• How do exponential size solutions arise in semidefinite programming?   G. Pataki, A. Touzov
  Submitted
  Talk at the Fields Institute, May 11, 2021    Poster talk at the MIP 2021 conference, May 24, 2021 2nd prize to Alex Touzov
• 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