# 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*