Publications - M. J. Todd

834. M.J. Todd, ``The Affine-Scaling Direction for Linear Programming is a Limit of Projective-Scaling Directions'' (Dec. 88). Linear Algebra and its Applications 152 (1991) 93-105.

836. M.J. Todd, ``Probabilistic Models for Linear Programming'' (Feb. 89). Mathematics of Operations Research 16 (1991) 671-693. Erratum.

857. M.J. Todd, ``The Effects of Degeneracy and Null and Unbounded Variables on Variants of Karmarkar's Linear Programming Algorithm'' (Aug. 89). In Large-Scale Numerical Optimization (T.F. Coleman and Y. Li, eds.), SIAM, Philadelphia, 1990, 81-91.

862. C.C. Gonzaga and M.J. Todd, ``An $O( \sqrt{n}L)$-Iteration Large-Step Primal-Dual Affine Algorithm for Linear Programming'' (Sept. 89). SIAM Journal on Optimization 2 (1992) 349-359.

877. M.J. Todd, ``On Combined Phase 1 - Phase 2 Projective Methods for Linear Programming'' (Dec. 89). Algorithmica 9 (1993) 64-83.

878. S. Mizuno, M.J. Todd, and Y. Ye, ``Anticipated Behavior of Path-Following Algorithms for Linear Programming'' (Dec. 89).

879. M.J. Todd, ``Anticipated Behavior of Karmarkar's Algorithm'' (Dec. 89).

882. S. Mizuno, M.J. Todd, and Y. Ye, ``Anticipated Behavior of Long-Step Algorithms for Linear Programming.`` (Jan. 90). TR882.ps.Z

893. L.G. Khachiyan and M.J. Todd, ``On the complexity of approximating the maximal inscribed ellipsoid for a polytope'' (Feb. 90). Mathematical Programming 61 (1993) 137-159.

903. M.J. Todd, ``A low-complexity interior-point algorithm for linear programming'' (May 90). SIAM Journal on Optimization 2 (1992) 198-209.

907. M.J. Todd, ``Combining phase I and phase II in a potential reduction algorithm for linear programming'' (July 90). Mathematical Programming 59 (1993) 133-150.

944. S. Mizuno, M.J. Todd, and Y. Ye, ``On adaptive-step primal-dual interior-point algorithms for linear programming'' (Oct. 90). Mathematics of Operations Research 18 (1993) 964-981.

946. M.J. Todd and L. Tunçel, ``A new triangulation for simplicial algorithms'' (Dec. 90). SIAM Journal on Discrete Mathematics 6 (1993) 167-180. TR946.ps.Z

950. M.J. Todd, ``Projected scaled steepest descent in Kojima-Mizuno-Yoshise's potential reduction algorithm for the linear complementarity problem'' (Dec. 90).

952. M.J. Todd and J.-P. Vial, ``Todd's low-complexity algorithm is a predictor-corrector path-following method'' (Dec. 90). Operations Research Letters 11 (1992) 199-207.

958. M.J. Todd, ``Playing with interior points'' (Feb. 91). COAL Newsletter of the Mathematical Programming Society 19 (1991) 17-25.

964. M.J. Todd, ``Another variational derivation of a self-scaling Quasi-Newton update formula'' (4/91).

978. M.J. Todd, ``Interior-point algorithms for semi-infinite programming'' (8/91). Mathematical Programming 65 (1994) 217-245.

995. M.J. Todd, ``Another derivation of the Karmarkar direction for linear programming'' (12/91). TR995.ps.Z Abstract

997. A. Liao and M.J. Todd, ``The ellipsoid algorithm using parallel cuts'' (1/92). Computational Optimization and Applications 2 (1993) 299-316.

1007. Y. Ye, M.J. Todd, and S. Mizuno, ``An $O(\sqrt{n}L$)-Iteration Homogeneous and Self-dual Linear Programming Algorithm'' (6/92). Mathematics of Operations Research 19 (1994) 53-67. Abstract

1014. S. Mizuno, M.J. Todd, and L. Tunçel, ``Monotonicity of Primal and Dual Objective Values in Primal-dual Interior Point Algorithms'' (7/92). SIAM Journal on Optimization 4 (1994) 613-625. TR1014.ps.Z Abstract

1016. R.M. Freund and M.J. Todd, ``Barrier Functions and Interior-Point Algorithms for Linear Programming with Zero-, One-, or Two-sided Bounds on the Variables'' (7/92). Condensed version in Mathematics of Operations Research 20 (1995) 415-440. TR1016.ps.Z Abstract

1023. S. Mizuno, M. Kojima, and M.J. Todd, ``Infeasible-Interior-Point Primal-Dual Potential-Reduction Algorithms for Linear Programming'' (8/92). SIAM Journal on Optimization 5 (1995) 52-67. TR1023.ps.Z Abstract

1031. L. Tunçel and M.J. Todd, ``Asymptotic Behavior of Interior-Point Methods: A View from Semi-Infinite Programming'' (9/92). Mathematics of Operations Research 21 (1996) 354-381. Abstract

1037. S. Mizuno, M.J. Todd and Y. Ye, ``A Surface of Analytic Centers and Infeasible- Interior-Point Algorithms for Linear Programming'' (1/93). Mathematics of Operations Research 20 (1995) 135-162. Abstract

1044. M.J. Todd, ``Analysis of Interior-Point Methods for Linear Programming Problems with Variable Upper Bounds'' (2/93). Advances in Optimization and Numerical Analysis, edited by Susana Gomez and Jean-Pierre Hennart, Mathematics and its Applications 275, Kluwer Academic Publishers, 1994, pp. 1-23. Abstract

1050. M.J. Todd, ``A Lower Bound on the Number of Iterations of Primal-Dual Interior-Point Methods for Linear Programming'' (3/93). In the proceedings of the 15th Biennial Conference on Numerical Analysis at Dundee, Numerical Analysis 1993 (G.A. Watson and D.F. Griffiths, eds.), Pitman Research Notes in Mathematics 303, Longman Press, 1994, pp. 237-259. Abstract

1064. A. Liao and M.J. Todd, ``Solving LP Problems Via Weighted Centers'' (8/93). SIAM Journal on Optimization 6 (1996) 933-960. TR1064.ps.Z Abstract

1067. M.J. Todd, ``Scaling, Shifting and Weighting in Interior-Point Methods'' (9/93). Computational Optimization and Applications 3 (1994) 305-315. Abstract

1071. R.H. Tütüncü and M.J. Todd, ``Reducing Horizontal Linear Complementarity Problems'' (10/93). Linear Algebra and its Applications 223/224 (1995) 717-729. Abstract

1082. M.J. Todd and Y. Ye, ``A Lower Bound on the Number of Iterations of Long-Step and Polynomial Interior-Point Linear Programming Algorithms'' (1/94). Annals of Operations Research 62 (1996) 233-252. Abstract

1091. Yu.E. Nesterov and M.J. Todd, ``Self-Scaled Barriers and Interior-Point Methods for Convex Programming'' (4/94). Mathematics of Operations Research 22 (1997) 1-42. Abstract

1097. S. Herzel and M.J. Todd, ``Two Interior-Point Algorithms for a Class of Convex Programming Problems'' (6/94). Optimization Methods and Software 5 (1995) 27-55. TR1097.ps.Z Abstract

1109. M.J. Todd and Y. Ye, ``Approximate Farkas Lemmas and Stopping Rules for Iterative Infeasible-Point Algorithms for Linear Programming'' (11/94). Mathematical Programming 81 (1998) 1-21. Abstract

1112. M.J. Todd, ``Potential-Reduction Methods in Mathematical Programming'' (1/95). Mathematical Programming 76 (1996) 3-45. Abstract

1125. Yu.E. Nesterov and M.J. Todd, ``Primal-Dual Interior-Point Methods for Self-Scaled Cones'' (5/95). SIAM Journal on Optimization 8 (1998) 324-364. TR1125.ps.Z Abstract

1135. L. Tunçel and M.J. Todd, ``On the Interplay Among Entropy, Variable Metrics and Potential Functions in Interior-Point Algorithms'' (9/95). Computational Optimization and Applications 8 (1997) 5-19. Abstract

1154. M.J. Todd, K.C. Toh, and R.H. Tütüncü, ``On the Nesterov-Todd Direction in Semidefinite Programming'' (3/96). SIAM Journal on Optimization 8 (1998) 769-796. TR1154.ps.Z Abstract

1156. Yu.E. Nesterov, M.J. Todd, and Y. Ye, ``Infeasible-Start Primal-Dual Dethods and Infeasibility Detectors for Nonlinear Programming Problems'' (4/96). Mathematical Programming 84 (1999) 227-267. Abstract

1170. M.J. Todd, ``On Adjusting Parameters in Homotopy Methods for Linear Programming'' (7/96). TR1170.ps.Z Abstract. In: Approximation Theory and Optimization, edited by M. Buhmann and A. Iserles, Cambridge University Press, 1997, pp. 201--220.

1177. K.C. Toh, M.J. Todd, and R.H. Tütüncü, ``SDPT3 --- a Matlab Software Package for Semidefinite Programming'' (12/96). TR1177.ps.gz Abstract Matlab files in compressed tar format can be obtained from here. An earlier version of the guide appeared in Optimization Methods and Software 11 (1999) 545-581.

1205. M.J. Todd, ``A Study of Search Directions in Primal-Dual Interior-Point Methods for Semidefinite Programming'' (10/97). Optimization Methods and Software 11 (1999) 1-46. TR1205.ps.Z Abstract

M.J. Todd, Erratum to TR 836, ``Probabilistic Models for Linear Programming,'' Mathematics of Operations Research 16 (1991) 671-693.

1213. S. Mizuno and M.J. Todd, ``On two homogeneous self-dual approaches to linear programming and its extensions'' (7/98) (Mathematical Programming 89 (2001), 517--534, online here). The original publication is available on LINK at http://link.springer.de. TR1213.ps Abstract

1219. M.J. Todd, L. Tunçel, and Y. Ye, ``Probabilistic analysis of two complexity measures for linear programming problems'' (9/98) (Mathematical Programming 90 (2001), 59--69, online here). TR1219.ps Abstract

1238. M. Wagner and M.J. Todd, ``Least-change quasi-Newton updates for equality-constrained optimization'' (5/99) (Mathematical Programming, 87 (2000), 317--350, online here). Abstract

1253. E.A. Yildirim and M.J. Todd, ``Sensitivity analysis in linear programming and semidefinite programming using interior-point methods'' (11/99) (Mathematical Programming, 90 (2001), 229--261, online here). TR1253.ps Abstract

R.D.C. Monteiro and M.J. Todd, ``Path-following methods,'' in Handbook on Semidefinite Programming, H. Wolkowicz, R. Saigal, and L. Vandenberghe (eds.), Kluwer Academic Publishers, Boston-Dordrecht-London, 2000, pp. 267--306.

M.J. Todd,``The many facets of linear programming'' (7/00), (Mathematical Programming, 91 (2002), 417--436, online here). ps file.

1268. E.A. Yildirim and M.J. Todd, ``An interior-point approach to sensitivity analysis in degenerate linear programs'' (12/00) SIAM Journal on Optimization 12, pp. 692--714, 2002. TR1268.ps Abstract

M.J. Todd,``Semidefinite optimization'' (2/01) (in Acta Numerica 10 (2001), pp. 515--560), ps file.

R.H. Tütüncü, K.C. Toh, and M.J. Todd, ``Solving semidefinite-quadratic-linear programs using SDPT3'' (3/01) (to appear in Mathematical Programming; online here), compressed ps file.

1290. Yu.E. Nesterov and M.J. Todd, ``On the Riemannian geometry defined by self-concordant barriers and interior-point methods'' (7/01) Foundations of Computational Mathematics 2, pp 333--361, 2002. TR1290.ps Abstract

R.H. Tütüncü, K.C. Toh, and M.J. Todd, ``SDPT3 --- A MATLAB software package for semidefinite-quadratic-linear programming, Version 3.0'' (8/01), compressed ps file, compressed dvi file. Matlab files in compressed tar format can be obtained from here.

1339. J.S. Marron, M.J. Todd, and J. Ahn,, ``Distance Weighted Discrimination'' (7/02), pdf file.

1363. M.J. Todd, ``Detecting Infeasibility in Infeasible-Interior-Point Methods for Optimization'' (1/03). TR1363.ps Abstract

1381. B.K. Rangarajan and M.J. Todd, ``Convergence of infeasible-interior-point methods for self-scaled conic programming'' (10/03). TR1381.ps Abstract