Levent Tunçel

PUBLICATIONS

  1. 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).

  2. 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).

  3. 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.

  4. 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

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

  6. 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

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

  8. 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

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

  10. 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.

  11. 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.

  12. 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.

  13. 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

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

  15. 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.

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

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

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

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

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

  21. 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.

  22. 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.

  23. 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.

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

  25. 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.

  26. 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.

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

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

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

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

  31. 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.

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

  33. 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.

  34. 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.

  35. 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.

  36. 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.

  37. 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.

  38. 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.

  39. 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.

  40. 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.

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

  42. 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.

  43. C. B. Chua and L. Tunçel, Invariance and efficiency of convex representations, Mathematical Programming B 111 (2008) 113-140 corr2004-18.pdf. The original publication is available at http://www.springerlink.com.

  44. 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.

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

  46. Y. 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.

  47. 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

  48. L. Tunçel, Optimization based approaches to product pricing, Proc. IV. International Conference on Business, Management and Economics ICBME'2008, to appear icbme2008.pdf.

  49. 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.

  50. L. Tunçel, Polyhedral and Semidefinite Programming Methods in Combinatorial Optimization, Fields Institute Monograph Series, AMS, to appear.

  51. 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.

  52. L. Kong, L. Tunçel and N. Xiu, The Fischer-Burmeister complementarity function on Euclidean Jordan algebras, Pacific Journal of Optimization, to appear corr2007-17.pdf.

  53. R. Shioda, L. Tunçel and T. G. J. Myklebust, Maximum utility product pricing models and algorithms based on reservation prices, Computational Optimization and Applications, to appear corr2007-08.pdf journal-version.pdf.

    RESEARCH REPORTS

  54. 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.'')

  55. 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

  56. 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.'')

  57. 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 lecture.ps. lecture.pdf.

  58. 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.

  59. 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.

  60. R. Shioda, L. Tunçel and B. Hui, Applications of deterministic optimization techniques to some probabilistic choice models for product pricing using reservation prices, Research Report CORR 2007-02, Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario, Canada, February 2007 (revised: February 2009) corr2007-02.pdf.

  61. L. Tunçel and A. Nemirovski, Self-concordant barriers for convex approximations of structured convex sets, Research Report CORR 2007-03, Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario, Canada, February 2007 (revised: July 2008) corr2007-03.pdf.

  62. L. Kong, L. Tunçel and N. Xiu, Monotonicity of Löwner operators and its applications to symmetric cone complementarity problems, Research Report CORR 2007-07, Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario, Canada, April 2007 (revised: August 2007) corr2007-07.pdf.

  63. L. Tunçel and H. Wolkowicz, Strong duality and minimal representations for cone optimization, Research Report CORR 2008-07, Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario, Canada, August 2008 (revised: September 2008) corr2008-07.pdf.

  64. L. Kong, L. Tunçel and N. Xiu, Equivalent conditions for Jacobian nonsingularity in linear symmetric cone programming, Research Report CORR 2008-12, Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario, Canada, October 2008 (revised: June 2009) corr2008-12.pdf.

  65. L. Kong, L. Tunçel and N. Xiu, Homogeneous cone complementarity problems and P properties, April 2009 arXiv:0904.1827.pdf.

  66. Yu. Nesterov and L. Tunçel, Local quadratic convergence of polynomial-time interior-point methods for conic optimization problems, CORE Discussion Paper 2009/72, Center for Operations Research and Econometrics (CORE), Catholic University of Louvain (UCL), Belgium, November 2009 CORE-2009-72.pdf.