Levent Tunçel

PUBLICATIONS

  1. A. Abdi, G. Cornuéjols, B. Guenin and L. Tunçel, Clean clutters and dyadic fractional packings, SIAM Journal on Discrete Math. , to appear dyadic.pdf

  2. N. Kalantarova and L. Tunçel, On the spectral structure of Jordan-Kronecker products of symmetric and skew-symmetric matrices, Linear Algebra and its Applications 608 (2021) 343-362 arXiv:1805.09737.pdf The final publication is available at DOI

  3. M. Karimi and L. Tunçel, Primal-dual interior-point methods for domain-driven formulations, Mathematics of Operations Research 45 (2020) 591-621 arXiv:1804.06925.pdf The final publication is available at DOI

  4. M. K. de Carli Silva and L. Tunçel, A notion of total dual integrality for convex, semidefinite, and extended formulations, SIAM Journal on Discrete Math. 34 (2020) 470-496 arXiv:1801.09155.pdf The final publication is available at DOI

  5. P. S. Ravi and L. Tunçel, Approximation ratio of LD algorithm for multi-processor scheduling and the Coffman-Sethi conjecture, Information Processing Letters 159-160 (2020) article 105959 arXiv:1505.01005.pdf

  6. M. K. de Carli Silva and L. Tunçel, Strict complementarity in semidefinite optimization with elliptopes including the MaxCut SDP, SIAM Journal on Optimization 29 (2019) 2650-2676 arXiv:1806.01173.pdf The final publication is available at DOI

  7. V. Roshchina and L. Tunçel, Facially dual complete (nice) cones and lexicographic tangents, SIAM Journal on Optimization 29 (2019) 2363-2387 arXiv:1704.06368.pdf

  8. Y. H. (Gary) Au and L. Tunçel, Elementary polytopes with high lift-and-project ranks for strong positive semidefinite operators, Discrete Optimization 27 (2018) 103-129 arXiv:1608.07647.pdf The final publication is available at DOI

  9. M. Karimi, S. Moazeni and L. Tunçel, A utility theory based interactive approach to robustness in linear optimization, Journal of Global Optimization 70 (2018) 811-842 arXiv:1312.4489.pdf The final publication is available at Springer via DOI

  10. M. K. de Carli Silva and L. Tunçel, An axiomatic duality framework for the theta body and related convex corners, Mathematical Programming A 162 (2017) 283-322 arXiv:1412.2103.pdf. The final publication is available at Springer via DOI

  11. S. M. Bianchi, M. S. Escalante, G. L. Nasini and L. Tunçel, Lovász-Schrijver SDP-operator, near-perfect graphs and near-bipartite graphs, Mathematical Programming A 162 (2017) 201-223 arXiv:1411.2069.pdf. The final publication is available at Springer via DOI

  12. M. Karimi, S. Luo and L. Tunçel, Primal-dual entropy based interior-point algorithms for linear optimization, RAIRO Operations Research 51 (2017) 299-328 arXiv:1410.8226.pdf The final publication is available at DOI

  13. L. Tunçel, Polynomial optimization with a focus on hyperbolic polynomials, Oberwolfach Reports OWR-2017-14 (2017) 797-800 OWR-2017-14.pdf

  14. P. S. Ravi, L. Tunçel and M. Huang, Worst-case performance analysis of some approximation algorithms for minimizing makespan and flowtime, Journal of Scheduling 19 (2016) 547-561 arXiv:1312.3345.pdf The final publication is available at Springer via DOI

  15. Y. H. (Gary) Au and L. Tunçel, A comprehensive analysis of polyhedral lift-and-project methods, SIAM Journal on Discrete Math. 30 (2016) 411-451 arXiv:1312.5972.pdf

  16. A. Nayak, J. Sikora and L. Tunçel, A search for quantum coin-flipping protocols using optimization techniques, Mathematical Programming A 156 (2016) 581-613 arXiv:1403.0505.pdf, arXiv:1403.0505-supplemental-material.pdf, source codes. The final publication is available at Springer via DOI

  17. Yu. Nesterov and L. Tunçel, Local superlinear convergence of polynomial-time interior-point methods for hyperbolicity cone optimization problems, SIAM Journal on Optimization 26 (2016) 139-170 arXiv:1412.1857.pdf

  18. M. Muramatsu, H. Waki and L. Tunçel, Perturbed sums of squares theorem for polynomial optimization and its applications, Optimization Methods and Software 31 (2016) 134-156 arXiv:1304:0065.pdf.

  19. T. G. J. Myklebust, M. A. Sharpe and L. Tunçel, Efficient heuristic algorithms for maximum utility product pricing problems, Computers and Operations Research 69 (2016) 25-39 pricedown.pdf, source codes and data.

  20. M. K. de Carli Silva and L. Tunçel, Vertices of spectrahedra arising from the elliptope, the theta body, and their relatives, SIAM Journal on Optimization 25 (2015) 295-316 arXiv:1309.7415.pdf

  21. Y. Awate, G. Cornuéjols, B. Guenin and L. Tunçel, On the relative strength of families of intersection cuts arising from pairs of tableau constraints in mixed integer programs, Mathematical Programming A 150 (2015) 459-489 relative-strength-intersection-cuts.pdf. The final publication is available at Springer via DOI

  22. R. Shioda, L. Tunçel and B. Hui, Applications of deterministic optimization techniques to some probabilistic choice models for product pricing using reservation prices, Pacific Journal of Optimization 10 (2014) 767-808 LongVersionShioda-Tuncel-Hui.pdf.

  23. B. Guenin, J. Könemann and L. Tunçel, A Gentle Introduction to Optimization, Cambridge University Press, 2014.

  24. S. M. Bianchi, M. S. Escalante, G. L. Nasini and L. Tunçel, Some advances on Lovász-Schrijver semidefinite programming relaxations of the fractional stable set polytope, Discrete Appl. Math. 164 (2014) 460-469 BENT_DAM.pdf

  25. M. K. de Carli Silva and L. Tunçel, Optimization problems over unit distance representations of graphs, Electronic Journal of Combinatorics 20 (2013) #P43 arXiv:1010.6036.pdf errata.pdf

  26. S. M. Bianchi, M. S. Escalante, G. L. Nasini and L. Tunçel, Lovász-Schrijver SDP-operator and a superclass of near-perfect graphs, Electronic Notes on Discrete Mathematics 44 (2013) 339-344.

  27. L. Kong, L. Tunçel and N. Xiu, S-goodness for low-rank matrix recovery, Abstract and Applied Analysis 2013 (2013) arXiv:1106.3276.pdf

  28. L. Kong, L. Tunçel and N. Xiu, Existence and uniqueness of solutions for homogeneous cone complementarity problems, Journal of Optimization Theory and Applications 153 (2012) 357-376. The final publication is available at Springer via DOI

  29. L. Tunçel and H. Wolkowicz, Strong duality and minimal representations for cone optimization, Computational Optimization and Applications 53 (2012) 619-648 corr2008-07.pdf. The final publication is available at Springer via DOI

  30. L. Kong, L. Tunçel and N. Xiu, Monotonicity of Löwner operators and its applications to symmetric cone complementarity problems, Mathematical Programming A, 133 (2012) 327-336 corr2007-07.pdf. The final publication is available at Springer via DOI

  31. Y. H. (Gary) Au and L. Tunçel, Complexity Analyses of Bienstock-Zuckerberg and Lasserre Relaxations on the Matching and Stable Set Polytopes, Proceedings of the 15th International Conference on Integer Programming and Combinatoral Optimization (IPCO 2011) New York, NY, USA, June 15-17, 2011, Lecture Notes in Computer Science 6655, Springer 2011, pp. 14-26.

  32. S. M. Bianchi, M. S. Escalante, G. L. Nasini and L. Tunçel, Near-perfect graphs with polyhedral N_+(G), Electronic Notes on Discrete Mathematics 37 (2011) 393-398.

  33. S. M. Bianchi, M. S. Escalante, G. L. Nasini and L. Tunçel, Some advances on Lovász-Schrijver N_+(.) relaxations on the fractional stable set polytope, Electronic Notes on Discrete Mathematics 37 (2011) 189-194.

  34. L. Kong, L. Tunçel and N. Xiu, Equivalent conditions for Jacobian nonsingularity in linear symmetric cone programming, Journal of Optimization Theory and Applications 148 (2011) 364-389. corr2008-12.pdf. The final publication is available at Springer via DOI

  35. R. Shioda, L. Tunçel and T. G. J. Myklebust, Maximum utility product pricing models and algorithms based on reservation prices, Computational Optimization and Applications 48 (2011) 157-198. journal-version.pdf. The final publication is available at Springer via DOI

  36. L. Tunçel, Polyhedral and Semidefinite Programming Methods in Combinatorial Optimization, Fields Institute Monograph Series, AMS, Volume FIM/27, 2010. errata-additional-material.pdf

  37. L. Tunçel and A. Nemirovski, Self-concordant barriers for convex approximations of structured convex sets, Foundations of Computational Mathematics 10 (2010) 485-525 corr2007-03.pdf, article.

  38. L. Kong, L. Tunçel and N. Xiu, The Fischer-Burmeister complementarity function on Euclidean Jordan algebras, Pacific Journal of Optimization 6 (2010) 423--440 corr2007-17.pdf.

  39. L. Tunçel, Some applications of semidefinite optimization from an operations research viewpoint, Iranian Journal of Operations Research 1 (2009) 1-29 IOR-invited-survey.pdf.

  40. L. Kong, L. Tunçel and N. Xiu, Clarke generalized Jacobian of the projection onto symmetric cones, Set-Valued and Variational Analysis 17 (2009) 135-151 journal-version.pdf, initial-version.pdf The final publication is available at Springer via DOI

  41. Y. H. (Gary) Au and L. Tunçel, On the polyhedral lift-and-project methods and the fractional stable set polytope, Discrete Optimization 6 (2009) 206-213 corr2008-03.pdf.

  42. L. Kong, L. Tunçel and N. Xiu, Vector-valued implicit Lagrangian for symmetric cone complementarity problems, Asia-Pacific Journal of Operational Research 26 (2009) 199-233 corr2006-24r.pdf.

  43. G. Cornuéjols, B. Guenin and L. Tunçel, Lehman matrices, Journal of Combinatorial Theory B 99 (2009) 531-556 corr2006-18.pdf.

  44. L. Tunçel, Optimization based approaches to product pricing, Proc. IV. International Conference on Business, Management and Economics ICBME'2008, vol. II, pp. 93-102 icbme2008.pdf.

  45. M. Potaptchik, L. Tunçel and H. Wolkowicz, Large scale portfolio optimization with piecewise linear transaction costs, Optimization Methods and Software 23 (2008) 929-952 corr2006-19.pdf.

  46. C. B. Chua and L. Tunçel, Invariance and efficiency of convex representations, Mathematical Programming B 111 (2008) 113-140 corr2004-18.pdf. The final publication is available at Springer via DOI

  47. S.-P. Hong and L. Tunçel, Unification of lower-bound analyses of the lift-and-project rank of combinatorial optimization polyhedra, Discrete Appl. Math. 156 (2008) 25-41 corr2004-05.ps. corr2004-05.pdf.

  48. R. Shioda and L. Tunçel, Clustering via minimum volume ellipsoids, Computational Optimization and Applications 37 (2007) 247-295 corr2005-12.pdf.

  49. A. Li and L. Tunçel, Some applications of symmetric cone programming in financial mathematics, Transactions on Operational Research 17 (2006) 1-19 survey-TOR1.pdf.

  50. L. Tunçel and H. Wolkowicz, Strengthened existence and uniqueness conditions for search directions in semidefinite programming, Linear Algebra and its Applications 400 (2005) 31-60 corr2003-20.ps. corr2003-20.pdf.

  51. A. Nemirovski and L. Tunçel, ''Cone-free'' primal-dual path-following and potential reduction polynomial time interior-point methods, Mathematical Programming A 102 (2005) 261-294 corr2002-32.ps. corr2002-32.pdf.

  52. L. Lipták and L. Tunçel, Lift-and-project ranks and antiblocker duality, Operations Research Letters 33 (2005) 35-41 corr2003-16.ps. corr2003-16.pdf.

  53. H. J. Lara, C. C. Gonzaga and L. Tunçel, On the limiting properties of the affine-scaling directions, Transactions on Operational Research 16 (2004) 47-69 corr2003-24.ps. corr2003-24.pdf.

  54. V. A. Truong and L. Tunçel, Geometry of homogeneous convex cones, duality mapping, and optimal self-concordant barriers, Mathematical Programming A 100 (2004) 295-316 corr2002-15.ps, journal-version.pdf.

  55. L. Lipták and L. Tunçel, The stable set problem and the lift-and-project ranks of graphs, Mathematical Programming B 98 (2003) 319-353 corr2002-13.ps. corr2002-13.pdf.

  56. M. Kojima and L. Tunçel, Some fundamental properties of successive convex relaxation methods on LCP and related problems, Journal of Global Optimization 24 (2002) 333-348.

  57. M. Kojima and L. Tunçel, On the finite convergence of successive SDP relaxation methods, European Journal of Operational Research 143 (2002) 325-341.

  58. J. C. K. Ho and L. Tunçel, Reconciliation of various complexity and condition measures for linear programming problems and a generalization of Tardos' theorem, FOUNDATIONS OF COMPUTATIONAL MATHEMATICS, Proceedings of the Smalefest, World Scientific, 2002, pp. 93-147 corr2000-33.ps. corr2000-33.pdf.

  59. L. Tunçel, On the Slater condition for the SDP relaxations of nonconvex sets, Operations Research Letters 29 (2001) 181-186.

  60. M. X. Goemans and L. Tunçel, When does the positive semidefiniteness constraint help in lifting procedures?, Mathematics of Operations Research 26 (2001) 796-815.

  61. L. Tunçel, Generalization of primal-dual interior-point methods to convex optimization problems in conic form, Foundations of Computational Mathematics 1 (2001) 229-254.

  62. L. Tunçel and S. Xu, On homogeneous convex cones, the Caratheodory number, and the duality mapping, Mathematics of Operations Research 26 (2001) 234-247.

  63. L. Tunçel, Interior point methods for semidefinite programming, Encyclopedia of Optimization, C. A. Floudas, P. M. Pardalos (eds.), Kluwer Academic Publishers, Boston, MA, USA, 2001, Vol. III, pp. 1-5.

  64. M. J. Todd, L. Tunçel and Y. Ye, Characterizations, bounds, and probabilistic analysis of two complexity measures for linear programming problems, Mathematical Programming A 90 (2001) 59-69.

  65. G. Pataki and L. Tunçel, On the generic properties of convex optimization problems in conic form, Mathematical Programming A 89 (2001) 449-457.

  66. M. Kojima and L. Tunçel, Discretization and localization in successive convex relaxation methods for nonconvex quadratic optimization problems, Mathematical Programming A 89 (2000) 79-111.

  67. M. Kojima and L. Tunçel, Cones of matrices and successive convex relaxations of nonconvex sets, SIAM Journal on Optimization 10 (2000) 750-778 nonconvex.ps. nonconvex.pdf.

  68. L. Tunçel, Potential reduction and primal-dual methods, in Handbook of Semidefinite Programming: Theory, Algorithms and Applications , H. Wolkowicz, R. Saigal and L. Vandenberghe (eds.), Kluwer Academic Publishers, Boston, MA, USA, 2000, pp. 235-265.

  69. L. Tunçel, Approximating the complexity measure of Vavasis-Ye algorithm is NP-hard, Mathematical Programming A 86 (1999) 219-223.

  70. L. Tunçel, On the condition numbers for polyhedra in Karmarkar's form, Operations Research Letters 24 (1999) 149-155.

  71. T. Stephen and L. Tunçel, On a representation of the matching polytope via semidefinite liftings, Mathematics of Operations Research 24 (1999) 1-7.

  72. M. Kojima and L. Tunçel, Monotonicity of primal-dual interior-point algorithms for semidefinite programming problems, Optimization Methods and Software 10 (1998) 275-296.

  73. L. Tunçel, Primal-dual symmetry and scale invariance of interior-point algorithms for convex optimization, Mathematics of Operations Research 23 (1998) 708-718.

  74. A. Seifi and L. Tunçel, A constant-potential infeasible-start interior-point algorithm with computational experiments and applications, Computational Optimization and Applications 9 (1998) 107-152.

  75. O. Güler and L. Tunçel, Characterization of the barrier parameter of homogeneous convex cones, Mathematical Programming A 81 (1998) 55-76.

  76. M.V. Ramana, L. Tunçel and H. Wolkowicz, Strong duality for semidefinite programming, SIAM Journal on Optimization 7 (1997) 641-662. strong-duality.ps strong-duality.pdf

  77. L. Tunçel and M. J. Todd On the interplay among entropy, variable metrics and potential functions in interior-point algorithms, Computational Optimization and Applications 8 (1997) 5-19.

  78. J. Cheriyan, W. H. Cunningham, L. Tunçel, and Y. Wang, A linear programming and rounding approach to max 2-sat, Cliques, Coloring, and Satisfiability, D. S. Johnson and M. A. Trick (eds.), DIMACS Series on Discrete Mathematics and Theoretical Computer Science, American Mathematical Society 1996, pp. 395-414.

  79. L. Tunçel and M. J. Todd, Asymptotic behavior of interior-point methods: A view from semi-infinite programming, Mathematics of Operations Research 21 (1996) 354-381.

  80. L. Tunçel, On the convergence of primal-dual interior-point methods with wide neighborhoods, Computational Optimization and Applications 4 (1995) 139-158.

  81. A. Seifi, L. Tunçel and K. W. Hipel, An improved interior-point approach for use in reservoir operation, in Advances in Water Resources Technology and Management, G. Tsakiris and M. A. Santos (eds.), Balkema, Rotterdam, 1994, pp. 213-220. mrop.ps mrop.pdf

  82. L. Tunçel, Constant potential primal-dual algorithms: A framework, Mathematical Programming A 66 (1994) 145-159.

  83. S. Mizuno, M. J. Todd and L. Tunçel, Monotonicity of primal and dual objective values in primal-dual interior-point algorithms, SIAM Journal on Optimization 4 (1994) 613-625. monotonicity.ps monotonicity.pdf

  84. L. Tunçel, On the complexity of preflow-push algorithms for maximum flow problems, Algorithmica 11 (1994) 353-359.

  85. M. J. Todd and L. Tunçel, A new triangulation for simplicial algorithms, SIAM Journal on Discrete Math. 6 (1993) 167-180. triangulation.ps triangulation.pdf

  86. L. Tunçel and P. L. Jackson, On the convexity of a function related to the Wagner-Whitin model, Operations Research Letters 11 (1992) 255-259.

  87. Ö. Saatçioğlu, M. Denizel, N. Karabakal and L. Tunçel, Operations research and industrial engineering studies on the administration of Middle East Technical University, Turkish Journal of Industrial Engineering, Vol.1, No.2, (1989) pp. 3-7 (in Turkish).

  88. C. Öğüt and L. Tunçel, Planning with multiple objectives in export operations, Proceedings of the XI. National Operational Research Congress, Istanbul, Turkey, 1988 (in Turkish).

    RESEARCH REPORTS

  89. L. Tunçel, ``A note on the primal-dual affine-scaling algorithms,'' CCOP Report No. 92-08, Cornell University, May 1992. (Results of this note are included in the paper ``Constant potential primal-dual algorithms: A framework.'')

  90. L. Tunçel, ``A pseudo-polynomial complexity analysis for interior-point algorithms,'' Research Report 93-16, Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario, Canada, July 1993 (revised: November 1993). pseudo-poly.ps pseudo-poly.pdf

  91. L. Tunçel, Primal-dual potential reduction algorithms for semidefinite programming, Technical Report B-337, Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Tokyo, Japan, March 1998. (Initial version of the paper ``Potential reduction and primal-dual methods.'')

  92. L. Tunçel, Convex optimization: Barrier functions and interior-point methods, Technical Report B-336, Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Tokyo, Japan, March 1998. (Preliminary version of the monograph ``Convex optimization: Barrier functions and interior-point methods.'')

  93. L. Tunçel and S. Xu, Complexity analyses of discretized successive convex relaxation methods, Research Report CORR 99-37, Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario, Canada, September 1999 corr99-37.ps. corr99-37.pdf.

  94. H. J. Lara and L. Tunçel, Condition and complexity measures for infeasibility certificates of systems of linear inequalities and their sensitivity analysis, Research Report CORR 2002-10, Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario, Canada, May 2002 (revised: July 2002) corr2002-10.ps. corr2002-10.pdf.

  95. L. Kong, L. Tunçel and N. Xiu, Homogeneous cone complementarity problems and P properties, April 2009 (revised: November 2010) arXiv:0904.1827.pdf. (It appeared as ``Existence and uniqueness of solutions for homogeneous cone complementarity problems'' above.)

  96. M. K. de Carli Silva and L. Tunçel, Min-max theorems related to geometric representations of graphs and their SDPs, October 2010 arXiv:1010.6036.pdf (initial version of ``Optimization problems over unit distance representations of graphs'' listed above)

  97. L. Kong, L. Tunçel and N. Xiu, S-goodness for low-rank matrix recovery, translated from sparse signal recovery, June 2011 (revised: May 2012) arXiv:1106.3276.pdf (It appeared as ``S-goodness for low-rank matrix recovery'' above.)

  98. M. Karimi, S. Moazeni and L. Tunçel, An improvised approach to robustness in linear optimization, December 2013 (revised: March 2016) arXiv:1312.4489.pdf (It appeared as ``A utility theory based interactive approach to robustness in linear optimization'' above.)

  99. T. G. J. Myklebust and L. Tunçel, Interior-point algorithms for convex optimization based on primal-dual metrics, November 2014 (revised: April 2016) arXiv:1411.2129.pdf

  100. A. Nayak, J. Sikora and L. Tunçel, Quantum and classical coin-flipping protocols based on bit-commitment and their point games, April 2015 arXiv:1504.04217.pdf

  101. M. K. de Carli Silva and L. Tunçel, Pointed closed convex sets are the intersection of all rational supporting closed halfspaces, February 2018 arXiv:1802.03296.pdf

  102. M. Karimi and L. Tunçel, Primal-dual interior-point methods for domain-driven formulations: Algorithms, April 2018 (revised: October 2018) arXiv:1804.06925.pdf (It appeared as ``Primal-dual interior-point methods for domain-driven formulations'' above.)

  103. M. K. de Carli Silva and L. Tunçel, Strict complementarity in MaxCut SDP, June 2018 (revised: February 2019) arXiv:1806.01173.pdf (It appeared as ``Strict complementarity in semidefinite optimization with elliptopes including the MaxCut SDP '' above.)

  104. M. Karimi and L. Tunçel, Status determination by interior-point methods for convex optimization problems in domain-driven form, January 2019 arXiv:1901.07084.pdf

  105. M. Karimi and L. Tunçel, Domain-Driven Solver (DDS): a MATLAB based software package for convex optimization problems in domain-driven form, August 2019 arXiv:1908.03075.pdf, software

  106. Y. H. (Gary) Au, N. Lindzey, and L. Tunçel, Matchings, hypergraphs, association schemes, and semidefinite optimization, August 2020 arXiv:2008.08628.pdf

  107. A. Abdi, G. Cornuéjols, B. Guenin and L. Tunçel, Total dual dyadicness and dyadic generating sets, November 2021 arXiv:2111.05749.pdf

  108. A. Abdi, G. Cornuéjols, B. Guenin and L. Tunçel, Testing idealness in the filter oracle model, January 2022 Filter-oracle-complexity.pdf