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## Todd, Michael J.

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 Author ID: todd.michael-j Published as: Todd, M.; Todd, M. J.; Todd, Michael; Todd, Michael J. Homepage: https://people.orie.cornell.edu/miketodd/todd.html External Links: MGP · Wikidata · ResearchGate · dblp · GND
 Documents Indexed: 143 Publications since 1973, including 8 Books
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#### Co-Authors

 74 single-authored 9 Ye, Yinyu 7 Mizuno, Shinji 6 Tütüncü, Reha H. 5 Toh, Kim-Chuan 5 Tunçel, Levent 4 Nesterov, Yurii 3 Mitchell, John E. 3 Yildirim, Emre Alper 2 Ahipaşaoğlu, Selin Damla 2 Burrell, Bruce P. 2 Freund, Robert M. 2 Goldfarb, Donald 2 Liao, Aiping 2 Marron, James Stephen 2 Pinkus, Allan M. 1 Acar, Robert C. 1 Adler, Ilan 1 Ahn, Jeongyoun 1 Awoniyi, Samuel A. 1 Bland, Robert G. 1 Bradshaw, Andrew Philip 1 Cucker, Felipe 1 Duguay, Claude 1 Eaves, B. Curtis 1 Fostel, Ana 1 Gancarova, Martina 1 Gonzaga, Clovis C. 1 Gould, Floyd J. 1 Halmagyi, G. Michael 1 Ip, Chi Ming 1 Khachiyan, Leonid Genrikhovich 1 Kojima, Masakazu 1 Lagarias, Jeffrey C. 1 Liu, Yufeng 1 Magnussen, John S. 1 Megiddo, Nimrod 1 Monma, Clyde L. 1 Monteiro, Renato D. C. 1 Morris, Walter D. jun. 1 Nemhauser, George L. 1 Nemirovski, Arkadi S. 1 Pardo, Luis Miguel 1 Peitgen, Heinz-Otto 1 Qiao, Xingye 1 Rinnooy Kan, Alexander Hendrik George 1 Rovinsky, Robert B. 1 Saigal, Romesh 1 Scarf, Herbert E. 1 Schrijver, Alexander 1 Shoemaker, Christine A. 1 Süli, Endre E. 1 Sun, Peng 1 Taubman, David S. 1 Vial, Jean-Philippe 1 Wagner, Harvey Maurice 1 Wagner, Michael M. 1 Wang, Yufei 1 Wei, Victor K.-W. 1 Wright, Alden H. 1 Zhang, Hao Helen
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#### Serials

 20 Mathematics of Operations Research 20 Mathematical Programming. Series A. Series B 14 Mathematical Programming 8 SIAM Journal on Optimization 3 Operations Research 3 Operations Research Letters 3 Computational Optimization and Applications 3 Optimization Methods & Software 2 Journal of the American Statistical Association 2 Journal of Combinatorial Theory. Series B 2 SIAM Journal on Numerical Analysis 2 SIAM Journal on Algebraic and Discrete Methods 2 Algorithmica 2 SIAM Journal on Discrete Mathematics 2 Linear Algebra and its Applications 2 Bulletin of the American Mathematical Society. New Series 2 Acta Numerica 2 London Mathematical Society Lecture Note Series 1 Discrete Applied Mathematics 1 Discrete Mathematics 1 IMA Journal of Numerical Analysis 1 Journal of Combinatorial Theory. Series A 1 Journal of Mathematical Economics 1 Journal of Optimization Theory and Applications 1 Management Science 1 Mathematical Programming Study 1 Numerical Functional Analysis and Optimization 1 SIAM Journal on Control and Optimization 1 European Journal of Combinatorics 1 SIAM Journal on Matrix Analysis and Applications 1 Annals of Operations Research 1 Computational Geometry 1 ORSA Journal on Computing 1 SIAM Journal on Applied Mathematics 1 SIAM Review 1 Economic Theory 1 Revista Investigación Operacional 1 IEEE Transactions on Image Processing 1 Foundations of Computational Mathematics 1 Pacific Journal of Optimization 1 Management Science. Ser. A, Theory Series 1 Contemporary Mathematics 1 Handbooks in Operations Research and Management Science 1 Lecture Notes in Economics and Mathematical Systems 1 MOS/SIAM Series on Optimization
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#### Fields

 116 Operations research, mathematical programming (90-XX) 70 Numerical analysis (65-XX) 14 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 13 General topology (54-XX) 10 Computer science (68-XX) 8 Combinatorics (05-XX) 8 Convex and discrete geometry (52-XX) 7 Calculus of variations and optimal control; optimization (49-XX) 6 General and overarching topics; collections (00-XX) 5 Algebraic topology (55-XX) 5 Manifolds and cell complexes (57-XX) 3 Operator theory (47-XX) 3 Statistics (62-XX) 2 History and biography (01-XX) 2 Dynamical systems and ergodic theory (37-XX) 2 Approximations and expansions (41-XX) 1 Commutative algebra (13-XX) 1 Partial differential equations (35-XX) 1 Functional analysis (46-XX) 1 Differential geometry (53-XX) 1 Biology and other natural sciences (92-XX) 1 Information and communication theory, circuits (94-XX)

#### Citations contained in zbMATH

128 Publications have been cited 2,710 times in 1,868 Documents Cited by Year
SDPT3 – a MATLAB software package for semidefinite programming, version 1. 3. Zbl 0997.90060
Toh, K. C.; Todd, M. J.; Tütüncü, R. H.
1999
Solving semidefinite-quadratic-linear programs using SDPT3. Zbl 1030.90082
Tütüncü, R. H.; Toh, K. C.; Todd, M. J.
2003
Self-scaled barriers and interior-point methods for convex programming. Zbl 0871.90064
Nesterov, Yu. E.; Todd, M. J.
1997
Primal-dual interior-point methods for self-scaled cones. Zbl 0922.90110
Nesterov, Yu. E.; Todd, M. J.
1998
Semidefinite optimization. Zbl 1105.65334
Todd, M. J.
2001
On adaptive-step primal-dual interior-point algorithms for linear programming. Zbl 0810.90091
Mizuno, Shinji; Todd, Michael J.; Ye, Yinyu
1993
The computation of fixed points and applications. Zbl 0332.54003
Todd, Michael J.
1976
An $$O(\sqrt{n} L)$$-iteration homogeneous and self-dual linear programming algorithm. Zbl 0799.90087
Ye, Yinyu; Todd, Michael J.; Mizuno, Shinji
1994
On the Nesterov-Todd direction in semidefinite programming. Zbl 0913.90217
Todd, M. J.; Toh, K. C.; Tütüncü, R. H.
1998
An extension of Karmarkar’s algorithm for linear programming using dual variables. Zbl 0621.90048
Todd, Michael J.; Burrell, Bruce P.
1986
A centered projective algorithm for linear programming. Zbl 0722.90044
Todd, Michael J.; Ye, Yinyu
1990
The ellipsoid method: A survey. Zbl 0474.90056
Bland, Robert G.; Goldfarb, Donald; Todd, Michael J.
1981
On the Riemannian geometry defined by self-concordant barriers and interior-point methods. Zbl 1049.90127
Nesterov, Yu. E.; Todd, M. J.
2002
On the implementation and usage of SDPT3 – a Matlab software package for semidefinite-quadratic-linear programming, version 4.0. Zbl 1334.90117
Toh, Kim-Chuan; Todd, Michael J.; Tütüncü, Reha H.
2012
Distance-weighted discrimination. Zbl 1332.62213
Marron, J. S.; Todd, Michael J.; Ahn, Jeongyoun
2007
Convex resource allocation problems on directed acyclic graphs: Duality, complexity, special cases, and extensions. Zbl 0717.90080
Monma, Clyde L.; Schrijver, Alexander; Todd, Michael J.; Wei, Victor K.
1990
Extensions of Lemke’s algorithm for the linear complementarity problem. Zbl 0327.90018
Todd, M. J.
1976
A study of search directions in primal-dual interior-point methods for semidefinite programming. Zbl 0971.90109
Todd, M. J.
1999
On the complexity of approximating the maximal inscribed ellipsoid for a polytope. Zbl 0792.90088
Khachiyan, Leonid G.; Todd, Michael J.
1993
On Khachiyan’s algorithm for the computation of minimum-volume enclosing ellipsoids. Zbl 1151.90516
Todd, Michael J.; Yıldırım, E. Alper
2007
The many facets of linear programming. Zbl 1030.90051
Todd, Michael J.
2002
Infeasible-interior-point primal-dual potential-reduction algorithms for linear programming. Zbl 0832.90076
Mizuno, Shinji; Kojima, Masakazu; Todd, Michael J.
1995
Infeasible-start primal-dual methods and infeasibility detectors for nonlinear programming problems. Zbl 0971.90061
Nesterov, Yu.; Todd, M. J.; Ye, Y.
1999
Improving the convergence of fixed-point algorithms. Zbl 0399.65034
Todd, Michael J.
1978
Two new proofs of Afriat’s theorem. Zbl 1084.91032
Fostel, A.; Scarf, H. E.; Todd, M. J.
2004
On triangulations for computing fixed points. Zbl 0358.90047
Todd, Michael J.
1976
Solving combinatorial optimization problems using Karmarkar’s algorithm. Zbl 0763.90074
Mitchell, John E.; Todd, Michael J.
1992
Linear convergence of a modified Frank-Wolfe algorithm for computing minimum-volume enclosing ellipsoids. Zbl 1146.90047
Ahipasaoglu, S. Damla; Sun, Peng; Todd, Michael J.
2008
Improved bounds and containing ellipsoids in Karmarkar’s linear programming algorithm. Zbl 0665.90059
Todd, Michael J.
1988
Efficient acceleration techniques for fixed point algorithms. Zbl 0396.65022
Saigal, Romesh; Todd, M. J.
1978
Orientation in complementary pivot algorithms. Zbl 0457.90074
Todd, Michael J.
1976
Inexact primal-dual path-following algorithms for a special class of convex quadratic SDP and related problems. Zbl 1136.90026
Toh, K. C.; Tütüncü, R. H.; Todd, M. J.
2007
Interior-point methods for optimization. Zbl 1160.65027
Nemirovski, Arkadi S.; Todd, Michael J.
2008
Recent developments and new directions in linear programming. Zbl 0683.90044
Todd, Michael J.
1989
Polynomial expected behavior of a pivoting algorithm for linear complementarity and linear programming problems. Zbl 0613.90094
Todd, Michael J.
1986
A constructive proof of Tucker’s combinatorial lemma. Zbl 0462.05026
Freund, Robert M.; Todd, Michael J.
1981
Weighted distance weighted discrimination and its asymptotic properties. Zbl 1397.62227
Qiao, Xingye; Zhang, Hao Helen; Liu, Yufeng; Todd, Michael J.; Marron, J. S.
2010
An improved Kalai-Kleitman bound for the diameter of a polyhedron. Zbl 1316.52021
Todd, Michael J.
2014
A surface of analytic centers and primal-dual infeasible-interior-point algorithms for linear programming. Zbl 0834.90088
Mizuno, Shinji; Todd, Michael J.; Ye, Yinyu
1995
A Dantzig-Wolfe-like variant of Karmarkar’s interior-point linear programming algorithm. Zbl 0724.90037
Todd, Michael J.
1990
Containing and shrinking ellipsoids in the path-following algorithm. Zbl 0746.90049
Ye, Yinyu; Todd, Michael J.
1990
Optimization. Zbl 0688.90034
Nemhauser, G. L. (ed.); Rinnooy Kan, A. H. G. (ed.); Todd, M. J. (ed.)
1989
Linear quadratic programming in oriented matroids. Zbl 0555.05026
Todd, Michael J.
1985
Modifications and implementation of the ellipsoid algorithm for linear programming. Zbl 0477.90038
Goldfarb, Donald; Todd, Michael J.
1982
On convergence properties of algorithms for unconstrained minimization. Zbl 0686.65032
Todd, Michael J.
1989
Complementarity in oriented matroids. Zbl 0556.05016
Todd, Michael J.
1984
An $$O(\sqrt n L)$$-iteration large-step primal-dual affine algorithm for linear programming. Zbl 0783.90071
Gonzaga, C. C.; Todd, M. J.
1992
Reducing horizontal linear complementarity problems. Zbl 0835.90106
Tütüncü, Reha H.; Todd, Michael J.
1995
The monotonic bounded Hirsch conjecture is false for dimension at least 4. Zbl 0457.52006
Todd, Michael J.
1980
Probabilistic models for linear programming. Zbl 0751.90056
Todd, Michael J.
1991
On minimum volume ellipsoids containing part of a given ellipsoid. Zbl 0503.90065
Todd, Michael J.
1982
An implementation of the simplex method for linear programming problems with variable upper bounds. Zbl 0477.90039
Todd, Michael J.
1982
Traversing large pieces of linearity in algorithms that solve equations by following piecewise-linear paths. Zbl 0441.90111
Todd, Michael J.
1980
Characterizations, bounds, and probabilistic analysis of two complexity measures for linear programming problems. Zbl 0978.90069
Todd, Michael J.; Tunçel, Levent; Ye, Yinyu
2001
On Anstreicher’s combined phase I-phase II projective algorithm for linear programming. Zbl 0773.90049
Todd, Michael J.
1992
A generalized complementary pivoting algorithm. Zbl 0285.90053
Todd, Michael J.
1974
A variable-dimension simplicial algorithm for antipodal fixed-point theorems. Zbl 0456.65024
Todd, Michael J.; Wright, Alden H.
1980
Sensitivity analysis in linear programming and semidefinite programming using interior-point methods. Zbl 1017.90110
Yıldırım, E. Alper; Todd, Michael J.
2001
A lower bound on the number of iterations of long-step primal-dual linear programming algorithms. Zbl 0848.90092
Todd, Michael J.; Ye, Yinyu
1996
Interior-point algorithms for semi-infinite programming. Zbl 0831.90114
Todd, Michael J.
1994
A low complexity interior-point algorithm for linear programming. Zbl 0811.90070
Todd, Michael J.
1992
A note on computing equilibria in economies with activity analysis models of production. Zbl 0432.90014
Todd, Michael J.
1979
Path-following methods. Zbl 0957.90523
Monteiro, Renato; Todd, Michael
2000
Potential-reduction methods in mathematical programming. Zbl 0881.90097
Todd, Michael J.
1997
Exploiting special structure in Karmarkar’s linear programming algorithm. Zbl 0649.90070
Todd, Michael J.
1988
Optimal conditioning and convergence in rank one quasi-Newton updates. Zbl 0638.65041
Ip, Chi Ming; Todd, Michael J.
1988
The ellipsoid method generates dual variables. Zbl 0582.90070
Burrell, Bruce P.; Todd, Michael J.
1985
Union Jack triangulations. Zbl 0424.90084
Todd, Michael J.
1977
Minimum-volume ellipsoids. Theory and algorithms. Zbl 1360.90006
Todd, Michael J.
2016
An interior-point approach to sensitivity analysis in degenerate linear programs. Zbl 1008.90064
Yildirim, E. Alper; Todd, Michael J.
2002
Combining phase I and phase II in a potential reduction algorithm for linear programming. Zbl 0777.90030
Todd, Michael J.
1993
New results on the average behavior of simplex algorithms. Zbl 0545.90066
Adler, Ilan; Megiddo, Nimrod; Todd, Michael J.
1984
Large-scale linear programming: Geometry, working bases and factorizations. Zbl 0516.90051
Todd, Michael J.
1983
On the computational complexity of piecewise-linear homotopy algorithms. Zbl 0509.90071
Todd, Michael J.
1982
Exploiting structure in piecewise-linear homotopy algorithms for solving equations. Zbl 0433.90088
Todd, Michael J.
1980
Approximate Farkas lemmas and stopping rules for iterative infeasible-point algorithms for linear programming. Zbl 0949.90060
Todd, Michael J.; Ye, Yinyu
1998
The effects of degeneracy and null and unbounded variables on variants of Karmarkar’s linear programming algorithm. Zbl 0726.90054
Todd, Michael J.
1990
A variant of Karmarkar’s linear programming algorithm for problems with some unrestricted variables. Zbl 0667.65048
Mitchell, John E.; Todd, Michael J.
1989
Symmetry and positive definiteness in oriented matroids. Zbl 0649.05023
Morris, Walter D. jun.; Todd, Michael J.
1988
Quasi-Newton updates in abstract vector spaces. Zbl 0574.65044
Todd, Michael J.
1984
Homotopy methods and global convergence. (Proceedings of a NATO Advanced Research Institut on Homotopy Methods and Global Convergence, held June 3-6, 1981, in Porto Cervo, Sardinia). Zbl 0507.00009
Eaves, B. Curtis (ed.); Gould, Floyd J. (ed.); Peitgen, Heinz-Otto (ed.); Todd, Michael J. (ed.)
1983
Solving the generalized market area problem. Zbl 0492.90041
Todd, Michael J.
1978
Characterizing binary simplicial matroids. Zbl 0337.05021
Todd, Michael J.
1976
A combinatorial generalization of polytopes. Zbl 0295.05007
Todd, Michael J.
1976
Detecting infeasibility in infeasible-interior-point methods for optimization. Zbl 1142.90499
Todd, Michael J.
2004
On the interplay among entropy, variable metrics and potential functions in interior-point algorithms. Zbl 0880.90103
Tunçel, Levent; Todd, Michael J.
1997
Asymptotic behavior of interior-point methods: A view from semi-infinite programming. Zbl 0857.90085
Tunçel, Levent; Todd, Michael J.
1996
On combined phase 1-phase 2 projective methods for linear programming. Zbl 0767.90048
Todd, Michael J.; Wang, Yufei
1993
Todd’s low-complexity algorithm is a predictor-corrector path-following method. Zbl 0768.90055
Todd, M. J.; Vial, J.-P.
1992
Global and local convergence and monotonicity results for a recent variable-dimension simplicial algorithm. Zbl 0449.65021
Todd, Michael J.
1980
A quadratically-convergent fixed-point algorithm for economic equilibria and linearly constrained optimization. Zbl 0429.90081
Todd, Michael J.
1980
Optimal dissection of simplices. Zbl 0384.52008
Todd, Michael J.
1978
A modified Frank–Wolfe algorithm for computing minimum-area enclosing ellipsoidal cylinders: theory and algorithms. Zbl 1266.65035
Damla Ahipaşaoğlu, S.; Todd, Michael J.
2013
A robust robust optimization result. Zbl 1242.90249
Gancarova, Martina; Todd, Michael J.
2012
Barrier functions and interior-point algorithms for linear programming with zero-, one, or two-sided bounds on the variables. Zbl 0837.90083
Freund, Robert M.; Todd, Michael J.
1995
Theory and practice for interior-point methods. Zbl 0800.90700
Todd, Michael J.
1994
A lower bound on the number of iterations of an interior-point algorithm for linear programming. Zbl 0815.65081
Todd, M. J.
1994
A new triangulation for simplicial algorithms. Zbl 0778.65038
Todd, Michael J.; Tunçel, Levent
1993
An $$O(n^ 3L)$$ adaptive path following algorithm for a linear complementarity problem. Zbl 0745.90070
Mizuno, Shinji; Todd, Michael J.
1991
Mathematical developments arising from linear programming. Proceedings of the AMS-IMS-SIAM joint summer research conference held at Bowdoin College, Brunswick, Maine/USA, June 25 - July 1, 1988. Zbl 0722.00047
Lagarias, Jeffrey C. (ed.); Todd, Michael J. (ed.)
1990
Minimum-volume ellipsoids. Theory and algorithms. Zbl 1360.90006
Todd, Michael J.
2016
Computation, multiplicity, and comparative statics of Cournot equilibria in integers. Zbl 1347.91189
Todd, Michael J.
2016
An improved Kalai-Kleitman bound for the diameter of a polyhedron. Zbl 1316.52021
Todd, Michael J.
2014
Optimization of demand response through peak shaving. Zbl 1408.90181
Zakeri, G.; Craigie, D.; Philpott, A.; Todd, M.
2014
A modified Frank–Wolfe algorithm for computing minimum-area enclosing ellipsoidal cylinders: theory and algorithms. Zbl 1266.65035
Damla Ahipaşaoğlu, S.; Todd, Michael J.
2013
On the implementation and usage of SDPT3 – a Matlab software package for semidefinite-quadratic-linear programming, version 4.0. Zbl 1334.90117
Toh, Kim-Chuan; Todd, Michael J.; Tütüncü, Reha H.
2012
A robust robust optimization result. Zbl 1242.90249
Gancarova, Martina; Todd, Michael J.
2012
Book review of: George B. Dantzig, The basic George B. Dantzig. Zbl 1292.00042
Todd, Michael J.
2011
Weighted distance weighted discrimination and its asymptotic properties. Zbl 1397.62227
Qiao, Xingye; Zhang, Hao Helen; Liu, Yufeng; Todd, Michael J.; Marron, J. S.
2010
Foundations of computational mathematics, Hong Kong, China, 2008. Selected papers based on the presentations at the international conference of the Society for the Foundations of Computational Mathematics (FoCM), June 16–26, 2008. Zbl 1170.13001
Cucker, Felipe (ed.); Pinkus, Allan (ed.); Todd, Michael J. (ed.)
2009
Largest dual ellipsoids inscribed in dual cones. Zbl 1165.90025
Todd, M. J.
2009
Linear convergence of a modified Frank-Wolfe algorithm for computing minimum-volume enclosing ellipsoids. Zbl 1146.90047
Ahipasaoglu, S. Damla; Sun, Peng; Todd, Michael J.
2008
Interior-point methods for optimization. Zbl 1160.65027
Nemirovski, Arkadi S.; Todd, Michael J.
2008
Dual versus primal-dual interior-point methods for linear and conic programming. Zbl 1163.90797
Todd, M. J.
2008
Distance-weighted discrimination. Zbl 1332.62213
Marron, J. S.; Todd, Michael J.; Ahn, Jeongyoun
2007
On Khachiyan’s algorithm for the computation of minimum-volume enclosing ellipsoids. Zbl 1151.90516
Todd, Michael J.; Yıldırım, E. Alper
2007
Inexact primal-dual path-following algorithms for a special class of convex quadratic SDP and related problems. Zbl 1136.90026
Toh, K. C.; Tütüncü, R. H.; Todd, M. J.
2007
Two new proofs of Afriat’s theorem. Zbl 1084.91032
Fostel, A.; Scarf, H. E.; Todd, M. J.
2004
Detecting infeasibility in infeasible-interior-point methods for optimization. Zbl 1142.90499
Todd, Michael J.
2004
Solving semidefinite-quadratic-linear programs using SDPT3. Zbl 1030.90082
Tütüncü, R. H.; Toh, K. C.; Todd, M. J.
2003
On the Riemannian geometry defined by self-concordant barriers and interior-point methods. Zbl 1049.90127
Nesterov, Yu. E.; Todd, M. J.
2002
The many facets of linear programming. Zbl 1030.90051
Todd, Michael J.
2002
An interior-point approach to sensitivity analysis in degenerate linear programs. Zbl 1008.90064
Yildirim, E. Alper; Todd, Michael J.
2002
Semidefinite optimization. Zbl 1105.65334
Todd, M. J.
2001
Characterizations, bounds, and probabilistic analysis of two complexity measures for linear programming problems. Zbl 0978.90069
Todd, Michael J.; Tunçel, Levent; Ye, Yinyu
2001
Sensitivity analysis in linear programming and semidefinite programming using interior-point methods. Zbl 1017.90110
Yıldırım, E. Alper; Todd, Michael J.
2001
On two homogeneous self-dual approaches to linear programming and its extensions. Zbl 1098.90530
Mizuno, Shinji; Todd, Michael J.
2001
Path-following methods. Zbl 0957.90523
Monteiro, Renato; Todd, Michael
2000
Least-change quasi-Newton updates for equality-constrained optimization. Zbl 0970.90120
Wagner, Michael; Todd, Michael J.
2000
SDPT3 – a MATLAB software package for semidefinite programming, version 1. 3. Zbl 0997.90060
Toh, K. C.; Todd, M. J.; Tütüncü, R. H.
1999
A study of search directions in primal-dual interior-point methods for semidefinite programming. Zbl 0971.90109
Todd, M. J.
1999
Infeasible-start primal-dual methods and infeasibility detectors for nonlinear programming problems. Zbl 0971.90061
Nesterov, Yu.; Todd, M. J.; Ye, Y.
1999
Primal-dual interior-point methods for self-scaled cones. Zbl 0922.90110
Nesterov, Yu. E.; Todd, M. J.
1998
On the Nesterov-Todd direction in semidefinite programming. Zbl 0913.90217
Todd, M. J.; Toh, K. C.; Tütüncü, R. H.
1998
Approximate Farkas lemmas and stopping rules for iterative infeasible-point algorithms for linear programming. Zbl 0949.90060
Todd, Michael J.; Ye, Yinyu
1998
Erratum: Probabilistic models for linear programming. Zbl 0977.90032
Todd, M. J.
1998
Self-scaled barriers and interior-point methods for convex programming. Zbl 0871.90064
Nesterov, Yu. E.; Todd, M. J.
1997
Potential-reduction methods in mathematical programming. Zbl 0881.90097
Todd, Michael J.
1997
On the interplay among entropy, variable metrics and potential functions in interior-point algorithms. Zbl 0880.90103
Tunçel, Levent; Todd, Michael J.
1997
Mathematical programming. Zbl 0904.90155
Todd, Michael J.
1997
A lower bound on the number of iterations of long-step primal-dual linear programming algorithms. Zbl 0848.90092
Todd, Michael J.; Ye, Yinyu
1996
Asymptotic behavior of interior-point methods: A view from semi-infinite programming. Zbl 0857.90085
Tunçel, Levent; Todd, Michael J.
1996
Solving LP problems via weighted centers. Zbl 0872.65049
Liao, Aiping; Todd, Michael J.
1996
Infeasible-interior-point primal-dual potential-reduction algorithms for linear programming. Zbl 0832.90076
Mizuno, Shinji; Kojima, Masakazu; Todd, Michael J.
1995
A surface of analytic centers and primal-dual infeasible-interior-point algorithms for linear programming. Zbl 0834.90088
Mizuno, Shinji; Todd, Michael J.; Ye, Yinyu
1995
Reducing horizontal linear complementarity problems. Zbl 0835.90106
Tütüncü, Reha H.; Todd, Michael J.
1995
Barrier functions and interior-point algorithms for linear programming with zero-, one, or two-sided bounds on the variables. Zbl 0837.90083
Freund, Robert M.; Todd, Michael J.
1995
An $$O(\sqrt{n} L)$$-iteration homogeneous and self-dual linear programming algorithm. Zbl 0799.90087
Ye, Yinyu; Todd, Michael J.; Mizuno, Shinji
1994
Interior-point algorithms for semi-infinite programming. Zbl 0831.90114
Todd, Michael J.
1994
Theory and practice for interior-point methods. Zbl 0800.90700
Todd, Michael J.
1994
A lower bound on the number of iterations of an interior-point algorithm for linear programming. Zbl 0815.65081
Todd, M. J.
1994
Scaling, shifting and weighting in interior-point methods. Zbl 0924.90112
Todd, Michael J.
1994
Analysis of interior-point methods for linear programming problems with variable upper bounds. Zbl 0823.90086
Todd, Michael J.
1994
Monotonicity of primal and dual objective values in primal-dual interior- point algorithms. Zbl 0827.90108
Mizuno, Shinji; Todd, Michael J.; Tunçel, Levent
1994
On adaptive-step primal-dual interior-point algorithms for linear programming. Zbl 0810.90091
Mizuno, Shinji; Todd, Michael J.; Ye, Yinyu
1993
On the complexity of approximating the maximal inscribed ellipsoid for a polytope. Zbl 0792.90088
Khachiyan, Leonid G.; Todd, Michael J.
1993
Combining phase I and phase II in a potential reduction algorithm for linear programming. Zbl 0777.90030
Todd, Michael J.
1993
On combined phase 1-phase 2 projective methods for linear programming. Zbl 0767.90048
Todd, Michael J.; Wang, Yufei
1993
A new triangulation for simplicial algorithms. Zbl 0778.65038
Todd, Michael J.; Tunçel, Levent
1993
Solving combinatorial optimization problems using Karmarkar’s algorithm. Zbl 0763.90074
Mitchell, John E.; Todd, Michael J.
1992
An $$O(\sqrt n L)$$-iteration large-step primal-dual affine algorithm for linear programming. Zbl 0783.90071
Gonzaga, C. C.; Todd, M. J.
1992
On Anstreicher’s combined phase I-phase II projective algorithm for linear programming. Zbl 0773.90049
Todd, Michael J.
1992
A low complexity interior-point algorithm for linear programming. Zbl 0811.90070
Todd, Michael J.
1992
Todd’s low-complexity algorithm is a predictor-corrector path-following method. Zbl 0768.90055
Todd, M. J.; Vial, J.-P.
1992
Probabilistic models for linear programming. Zbl 0751.90056
Todd, Michael J.
1991
An $$O(n^ 3L)$$ adaptive path following algorithm for a linear complementarity problem. Zbl 0745.90070
Mizuno, Shinji; Todd, Michael J.
1991
The affine-scaling direction for linear programming is a limit of projective-scaling directions. Zbl 0729.65041
Todd, Michael J.
1991
A centered projective algorithm for linear programming. Zbl 0722.90044
Todd, Michael J.; Ye, Yinyu
1990
Convex resource allocation problems on directed acyclic graphs: Duality, complexity, special cases, and extensions. Zbl 0717.90080
Monma, Clyde L.; Schrijver, Alexander; Todd, Michael J.; Wei, Victor K.
1990
A Dantzig-Wolfe-like variant of Karmarkar’s interior-point linear programming algorithm. Zbl 0724.90037
Todd, Michael J.
1990
Containing and shrinking ellipsoids in the path-following algorithm. Zbl 0746.90049
Ye, Yinyu; Todd, Michael J.
1990
The effects of degeneracy and null and unbounded variables on variants of Karmarkar’s linear programming algorithm. Zbl 0726.90054
Todd, Michael J.
1990
Mathematical developments arising from linear programming. Proceedings of the AMS-IMS-SIAM joint summer research conference held at Bowdoin College, Brunswick, Maine/USA, June 25 - July 1, 1988. Zbl 0722.00047
Lagarias, Jeffrey C. (ed.); Todd, Michael J. (ed.)
1990
Recent developments and new directions in linear programming. Zbl 0683.90044
Todd, Michael J.
1989
Optimization. Zbl 0688.90034
Nemhauser, G. L. (ed.); Rinnooy Kan, A. H. G. (ed.); Todd, M. J. (ed.)
1989
On convergence properties of algorithms for unconstrained minimization. Zbl 0686.65032
Todd, Michael J.
1989
A variant of Karmarkar’s linear programming algorithm for problems with some unrestricted variables. Zbl 0667.65048
Mitchell, John E.; Todd, Michael J.
1989
Improved bounds and containing ellipsoids in Karmarkar’s linear programming algorithm. Zbl 0665.90059
Todd, Michael J.
1988
Exploiting special structure in Karmarkar’s linear programming algorithm. Zbl 0649.90070
Todd, Michael J.
1988
Optimal conditioning and convergence in rank one quasi-Newton updates. Zbl 0638.65041
Ip, Chi Ming; Todd, Michael J.
1988
Symmetry and positive definiteness in oriented matroids. Zbl 0649.05023
Morris, Walter D. jun.; Todd, Michael J.
1988
Polynomial algorithms for linear programming. Zbl 0651.90046
Todd, Michael J.
1988
An extension of Karmarkar’s algorithm for linear programming using dual variables. Zbl 0621.90048
Todd, Michael J.; Burrell, Bruce P.
1986
Polynomial expected behavior of a pivoting algorithm for linear complementarity and linear programming problems. Zbl 0613.90094
Todd, Michael J.
1986
The symmetric rank-one quasi-Newton method is a space-dilation subgradient algorithm. Zbl 0604.90113
Todd, Michael J.
1986
Linear quadratic programming in oriented matroids. Zbl 0555.05026
Todd, Michael J.
1985
The ellipsoid method generates dual variables. Zbl 0582.90070
Burrell, Bruce P.; Todd, Michael J.
1985
“Fat” triangulations, or solving certain nonconvex matrix optimization problems. Zbl 0588.90074
Todd, Michael J.
1985
Complementarity in oriented matroids. Zbl 0556.05016
Todd, Michael J.
1984
New results on the average behavior of simplex algorithms. Zbl 0545.90066
Adler, Ilan; Megiddo, Nimrod; Todd, Michael J.
1984
Quasi-Newton updates in abstract vector spaces. Zbl 0574.65044
Todd, Michael J.
1984
J’: A new triangulation of $${\mathbb{R}}^ n$$. Zbl 0542.65027
Todd, Michael J.
1984
Large-scale linear programming: Geometry, working bases and factorizations. Zbl 0516.90051
Todd, Michael J.
1983
Homotopy methods and global convergence. (Proceedings of a NATO Advanced Research Institut on Homotopy Methods and Global Convergence, held June 3-6, 1981, in Porto Cervo, Sardinia). Zbl 0507.00009
Eaves, B. Curtis (ed.); Gould, Floyd J. (ed.); Peitgen, Heinz-Otto (ed.); Todd, Michael J. (ed.)
1983
An efficient simplicial algorithm for computing a zero of a convex union of smooth functions. Zbl 0493.90074
Awoniyi, Samuel A.; Todd, Michael J.
1983
Piecewise-linear homotopy algorithms for sparse systems of nonlinear equations. Zbl 0508.65019
Todd, Michael J.
1983
Modifications and implementation of the ellipsoid algorithm for linear programming. Zbl 0477.90038
Goldfarb, Donald; Todd, Michael J.
1982
On minimum volume ellipsoids containing part of a given ellipsoid. Zbl 0503.90065
Todd, Michael J.
1982
An implementation of the simplex method for linear programming problems with variable upper bounds. Zbl 0477.90039
Todd, Michael J.
1982
On the computational complexity of piecewise-linear homotopy algorithms. Zbl 0509.90071
Todd, Michael J.
1982
...and 28 more Documents
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#### Cited by 2,369 Authors

 49 Todd, Michael J. 43 Ye, Yinyu 37 Kheirfam, Behrouz 35 Terlaky, Tamás 33 Kojima, Masakazu 26 Roos, Cornelis 23 Liu, Hongwei 22 Wang, Guoqiang 20 Zangiabadi, Maryam 18 Potra, Florian-Alexandru 17 Bai, Yanqin 16 Boyd, Stephen Poythress 16 Ferreira, Orizon Pereira 16 Mizuno, Shinji 16 Toh, Kimchuan 15 Mansouri, Hossein 15 Shabtay, Dvir 15 Van der Laan, Gerard 14 Tunçel, Levent 14 Zhang, Shuzhong 13 Anstreicher, Kurt M. 13 Darvay, Zsolt 13 Freund, Robert M. 13 Monteiro, Renato D. C. 13 Tsuchiya, Takashi 12 Kim, Sunyoung 12 Liu, Changhe 12 Oliveira, Paulo Roberto 12 Vial, Jean-Philippe 12 Yang, Ximei 11 Goldfarb, Donald 11 Mitchell, John E. 11 Parrilo, Pablo A. 11 Sturm, Jos F. 11 Talman, Adolphus J. J. 11 Wolkowicz, Henry 11 Zhang, Yin 10 Goffin, Jean-Louis 10 Sun, Defeng 10 Yang, Zaifu 9 Marron, James Stephen 9 Pirhaji, Mohammad 9 Sun, Jie 9 Yamashita, Makoto 8 Asadi, Soodabeh 8 Gondzio, Jacek 8 Gonzaga, Clovis C. 8 Jarre, Florian 8 Lim, Yongdo 8 Muramatsu, Masakazu 8 Nemirovski, Arkadi S. 8 Peña, Javier F. 8 Salahi, Maziar 8 Toh, Kim-Chuan 7 Dang, Chuangyin 7 de Klerk, Etienne 7 Fang, Liang 7 Farhood, Mazen 7 Huang, Zheng-Hai 7 Kanno, Yoshihiro 7 Klep, Igor 7 Kortanek, Kenneth O. 7 Lasserre, Jean-Bernard 7 Lesaja, Goran 7 Megiddo, Nimrod 7 Nesterov, Yurii 7 Povh, Janez 7 Qi, Houduo 7 Qi, Liqun 7 Rendl, Franz 7 Steiner, George 7 Su, Francis Edward 7 Vandenberghe, Lieven 7 Vavasis, Stephen A. 7 Yamamoto, Yoshitsugu 7 Zhang, Yinkui 6 Açıkmeşe, Behçet 6 Al-Homidan, Suliman S. 6 Aoshima, Makoto 6 da Cruz Neto, João Xavier 6 D’Apuzzo, Marco 6 den Hertog, Dick 6 Deza, Antoine 6 Eaves, B. Curtis 6 Faybusovich, Leonid E. 6 Fukushima, Masao 6 Güler, Osman 6 Kaspi, Moshe 6 Mahdavi-Amiri, Nezam 6 Mansouri, Hosseino 6 Mansouri, Hossien 6 Mehrotra, Sanjay 6 Santos, Francisco 6 Sayadi Shahraki, M. 6 Shi, Zhenjun 6 Sikorski, Krzysztof A. 6 Talman, Dolf 6 Tran Dinh Quoc 6 Waki, Hayato 6 Wright, Stephen J. ...and 2,269 more Authors
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#### Cited in 281 Serials

 220 Mathematical Programming. Series A. Series B 108 Journal of Optimization Theory and Applications 83 Computational Optimization and Applications 73 Optimization Methods & Software 64 European Journal of Operational Research 61 Mathematical Programming 47 Linear Algebra and its Applications 46 Operations Research Letters 39 Annals of Operations Research 38 Optimization 38 SIAM Journal on Optimization 32 Journal of Global Optimization 31 Automatica 29 Applied Mathematics and Computation 29 Optimization Letters 26 Discrete Applied Mathematics 26 Computers & Operations Research 25 International Journal of Control 22 Numerical Algorithms 21 Journal of Computational and Applied Mathematics 20 Journal of Mathematical Analysis and Applications 17 Mathematical Programming Computation 14 Algorithmica 14 Optimization and Engineering 13 Numerical Functional Analysis and Optimization 12 Discrete Mathematics 12 Journal of Mathematical Economics 12 Systems & Control Letters 12 Journal of the Operations Research Society of China 11 Journal of Complexity 11 Mathematical Methods of Operations Research 11 RAIRO. Operations Research 10 Discrete & Computational Geometry 10 Economic Theory 10 Journal of Applied Mathematics and Computing 9 The Annals of Statistics 9 Journal of Combinatorial Theory. Series A 9 Applied Numerical Mathematics 9 Acta Mathematicae Applicatae Sinica. English Series 8 Mathematics of Operations Research 8 International Journal of Computer Mathematics 8 International Journal of Robust and Nonlinear Control 8 Journal of Combinatorial Optimization 8 Foundations of Computational Mathematics 7 Asia-Pacific Journal of Operational Research 7 Mathematical Problems in Engineering 7 Journal of Industrial and Management Optimization 6 Journal of the Franklin Institute 6 Mathematics of Computation 6 Journal of Statistical Planning and Inference 6 Theoretical Computer Science 6 European Journal of Combinatorics 6 Computational Statistics and Data Analysis 6 SIAM Journal on Scientific Computing 6 CEJOR. Central European Journal of Operations Research 6 Numerical Algebra, Control and Optimization 5 Computers & Mathematics with Applications 5 Applied Mathematics and Optimization 5 Journal of Economic Theory 5 Journal of Multivariate Analysis 5 Kybernetika 5 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 5 SIAM Journal on Computing 5 Journal of Scientific Computing 5 Machine Learning 5 Automation and Remote Control 5 Pattern Recognition 5 European Journal of Control 5 Journal of Inequalities and Applications 5 Journal of Scheduling 5 Acta Mathematica Sinica. English Series 5 Asian Journal of Control 4 International Journal for Numerical Methods in Engineering 4 Journal of the American Statistical Association 4 SIAM Journal on Algebraic and Discrete Methods 4 Statistical Science 4 Mathematical and Computer Modelling 4 Science in China. Series A 4 Japan Journal of Industrial and Applied Mathematics 4 Numerical Linear Algebra with Applications 4 INFORMS Journal on Computing 4 New Journal of Physics 4 The ANZIAM Journal 4 Journal of Machine Learning Research (JMLR) 4 4OR 4 Discrete Optimization 4 The Annals of Applied Statistics 3 Computer Methods in Applied Mechanics and Engineering 3 International Journal of Mathematical Education in Science and Technology 3 International Journal of Systems Science 3 Journal of Computational Physics 3 Information Sciences 3 Journal of Combinatorial Theory. Series B 3 Journal of Computer and System Sciences 3 Operations Research 3 Topology and its Applications 3 Advances in Applied Mathematics 3 Journal of Information & Optimization Sciences 3 Combinatorica 3 Computer Aided Geometric Design ...and 181 more Serials
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#### Cited in 53 Fields

 1,444 Operations research, mathematical programming (90-XX) 427 Numerical analysis (65-XX) 144 Computer science (68-XX) 138 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 129 Systems theory; control (93-XX) 103 Calculus of variations and optimal control; optimization (49-XX) 99 Statistics (62-XX) 78 Convex and discrete geometry (52-XX) 70 Combinatorics (05-XX) 69 Linear and multilinear algebra; matrix theory (15-XX) 38 General topology (54-XX) 36 Operator theory (47-XX) 23 Algebraic topology (55-XX) 21 Biology and other natural sciences (92-XX) 20 Information and communication theory, circuits (94-XX) 19 Mechanics of deformable solids (74-XX) 18 Probability theory and stochastic processes (60-XX) 15 Algebraic geometry (14-XX) 13 Ordinary differential equations (34-XX) 10 Nonassociative rings and algebras (17-XX) 10 Real functions (26-XX) 10 Approximations and expansions (41-XX) 9 Commutative algebra (13-XX) 9 Partial differential equations (35-XX) 9 Manifolds and cell complexes (57-XX) 8 Dynamical systems and ergodic theory (37-XX) 8 Functional analysis (46-XX) 8 Differential geometry (53-XX) 8 Global analysis, analysis on manifolds (58-XX) 7 Geometry (51-XX) 7 Quantum theory (81-XX) 6 Number theory (11-XX) 6 Mechanics of particles and systems (70-XX) 5 History and biography (01-XX) 5 Mathematical logic and foundations (03-XX) 5 Field theory and polynomials (12-XX) 5 Functions of a complex variable (30-XX) 4 General and overarching topics; collections (00-XX) 4 General algebraic systems (08-XX) 4 Fluid mechanics (76-XX) 4 Statistical mechanics, structure of matter (82-XX) 3 Associative rings and algebras (16-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Integral transforms, operational calculus (44-XX) 2 Mathematics education (97-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Group theory and generalizations (20-XX) 1 Topological groups, Lie groups (22-XX) 1 Measure and integration (28-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Abstract harmonic analysis (43-XX) 1 Integral equations (45-XX) 1 Optics, electromagnetic theory (78-XX)

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