Edit Profile (opens in new tab) Todd, Michael J. Compute Distance To: Compute Author ID: todd.michael-j Published as: Todd, Michael J.; Todd, M. J.; Todd, Michael Homepage: https://people.orie.cornell.edu/miketodd/todd.html External Links: MGP · Wikidata · ResearchGate · dblp · GND · IdRef Documents Indexed: 138 Publications since 1973, including 3 Books 5 Contributions as Editor Co-Authors: 59 Co-Authors with 67 Joint Publications 2,012 Co-Co-Authors all top 5 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 Craigie, D. 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 Wang, Yufei 1 Wei, Victor K.-W. 1 Wright, Alden H. 1 Zhang, Hao Helen all top 5 Serials 20 Mathematics of Operations Research 20 Mathematical Programming. Series A. Series B 14 Mathematical Programming 8 SIAM Journal on Optimization 4 Operations Research Letters 3 Operations Research 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 all top 5 Fields 117 Operations research, mathematical programming (90-XX) 70 Numerical analysis (65-XX) 15 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) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 128 Publications have been cited 2,835 times in 1,982 Documents Cited by ▼ Year ▼ SDPT3 – a MATLAB software package for semidefinite programming, version 1. 3. Zbl 0997.90060Toh, K. C.; Todd, M. J.; Tütüncü, R. H. 305 1999 Solving semidefinite-quadratic-linear programs using SDPT3. Zbl 1030.90082Tütüncü, R. H.; Toh, K. C.; Todd, M. J. 233 2003 Self-scaled barriers and interior-point methods for convex programming. Zbl 0871.90064Nesterov, Yu. E.; Todd, M. J. 201 1997 Primal-dual interior-point methods for self-scaled cones. Zbl 0922.90110Nesterov, Yu. E.; Todd, M. J. 192 1998 Semidefinite optimization. Zbl 1105.65334Todd, M. J. 165 2001 On adaptive-step primal-dual interior-point algorithms for linear programming. Zbl 0810.90091Mizuno, Shinji; Todd, Michael J.; Ye, Yinyu 150 1993 The computation of fixed points and applications. Zbl 0332.54003Todd, Michael J. 97 1976 An \(O(\sqrt{n} L)\)-iteration homogeneous and self-dual linear programming algorithm. Zbl 0799.90087Ye, Yinyu; Todd, Michael J.; Mizuno, Shinji 90 1994 On the Nesterov-Todd direction in semidefinite programming. Zbl 0913.90217Todd, M. J.; Toh, K. C.; Tütüncü, R. H. 83 1998 An extension of Karmarkar’s algorithm for linear programming using dual variables. Zbl 0621.90048Todd, Michael J.; Burrell, Bruce P. 75 1986 A centered projective algorithm for linear programming. Zbl 0722.90044Todd, Michael J.; Ye, Yinyu 63 1990 The ellipsoid method: A survey. Zbl 0474.90056Bland, Robert G.; Goldfarb, Donald; Todd, Michael J. 57 1981 On the Riemannian geometry defined by self-concordant barriers and interior-point methods. Zbl 1049.90127Nesterov, Yu. E.; Todd, M. J. 50 2002 On the implementation and usage of SDPT3 – a Matlab software package for semidefinite-quadratic-linear programming, version 4.0. Zbl 1334.90117Toh, Kim-Chuan; Todd, Michael J.; Tütüncü, Reha H. 50 2012 Distance-weighted discrimination. Zbl 1332.62213Marron, J. S.; Todd, Michael J.; Ahn, Jeongyoun 46 2007 Convex resource allocation problems on directed acyclic graphs: Duality, complexity, special cases, and extensions. Zbl 0717.90080Monma, Clyde L.; Schrijver, Alexander; Todd, Michael J.; Wei, Victor K. 37 1990 A study of search directions in primal-dual interior-point methods for semidefinite programming. Zbl 0971.90109Todd, M. J. 36 1999 Extensions of Lemke’s algorithm for the linear complementarity problem. Zbl 0327.90018Todd, M. J. 35 1976 On the complexity of approximating the maximal inscribed ellipsoid for a polytope. Zbl 0792.90088Khachiyan, Leonid G.; Todd, Michael J. 33 1993 On Khachiyan’s algorithm for the computation of minimum-volume enclosing ellipsoids. Zbl 1151.90516Todd, Michael J.; Yıldırım, E. Alper 30 2007 The many facets of linear programming. Zbl 1030.90051Todd, Michael J. 28 2002 Infeasible-start primal-dual methods and infeasibility detectors for nonlinear programming problems. Zbl 0971.90061Nesterov, Yu.; Todd, M. J.; Ye, Y. 27 1999 Infeasible-interior-point primal-dual potential-reduction algorithms for linear programming. Zbl 0832.90076Mizuno, Shinji; Kojima, Masakazu; Todd, Michael J. 25 1995 Improving the convergence of fixed-point algorithms. Zbl 0399.65034Todd, Michael J. 25 1978 Two new proofs of Afriat’s theorem. Zbl 1084.91032Fostel, A.; Scarf, H. E.; Todd, M. J. 25 2004 Linear convergence of a modified Frank-Wolfe algorithm for computing minimum-volume enclosing ellipsoids. Zbl 1146.90047Ahipasaoglu, S. Damla; Sun, Peng; Todd, Michael J. 24 2008 On triangulations for computing fixed points. Zbl 0358.90047Todd, Michael J. 23 1976 Solving combinatorial optimization problems using Karmarkar’s algorithm. Zbl 0763.90074Mitchell, John E.; Todd, Michael J. 22 1992 Weighted distance weighted discrimination and its asymptotic properties. Zbl 1397.62227Qiao, Xingye; Zhang, Hao Helen; Liu, Yufeng; Todd, Michael J.; Marron, J. S. 22 2010 Efficient acceleration techniques for fixed point algorithms. Zbl 0396.65022Saigal, Romesh; Todd, M. J. 19 1978 Orientation in complementary pivot algorithms. Zbl 0457.90074Todd, Michael J. 19 1976 Interior-point methods for optimization. Zbl 1160.65027Nemirovski, Arkadi S.; Todd, Michael J. 18 2008 Improved bounds and containing ellipsoids in Karmarkar’s linear programming algorithm. Zbl 0665.90059Todd, Michael J. 18 1988 A constructive proof of Tucker’s combinatorial lemma. Zbl 0462.05026Freund, Robert M.; Todd, Michael J. 18 1981 Inexact primal-dual path-following algorithms for a special class of convex quadratic SDP and related problems. Zbl 1136.90026Toh, K. C.; Tütüncü, R. H.; Todd, M. J. 18 2007 Polynomial expected behavior of a pivoting algorithm for linear complementarity and linear programming problems. Zbl 0613.90094Todd, Michael J. 17 1986 A Dantzig-Wolfe-like variant of Karmarkar’s interior-point linear programming algorithm. Zbl 0724.90037Todd, Michael J. 14 1990 Containing and shrinking ellipsoids in the path-following algorithm. Zbl 0746.90049Ye, Yinyu; Todd, Michael J. 14 1990 Linear quadratic programming in oriented matroids. Zbl 0555.05026Todd, Michael J. 14 1985 Complementarity in oriented matroids. Zbl 0556.05016Todd, Michael J. 14 1984 Recent developments and new directions in linear programming. Zbl 0683.90044Todd, Michael J. 14 1989 Modifications and implementation of the ellipsoid algorithm for linear programming. Zbl 0477.90038Goldfarb, Donald; Todd, Michael J. 14 1982 An improved Kalai-Kleitman bound for the diameter of a polyhedron. Zbl 1316.52021Todd, Michael J. 13 2014 On convergence properties of algorithms for unconstrained minimization. Zbl 0686.65032Todd, Michael J. 13 1989 A surface of analytic centers and primal-dual infeasible-interior-point algorithms for linear programming. Zbl 0834.90088Mizuno, Shinji; Todd, Michael J.; Ye, Yinyu 13 1995 An \(O(\sqrt n L)\)-iteration large-step primal-dual affine algorithm for linear programming. Zbl 0783.90071Gonzaga, C. C.; Todd, M. J. 12 1992 The monotonic bounded Hirsch conjecture is false for dimension at least 4. Zbl 0457.52006Todd, Michael J. 12 1980 Reducing horizontal linear complementarity problems. Zbl 0835.90106Tütüncü, Reha H.; Todd, Michael J. 11 1995 On minimum volume ellipsoids containing part of a given ellipsoid. Zbl 0503.90065Todd, Michael J. 10 1982 Probabilistic models for linear programming. Zbl 0751.90056Todd, Michael J. 10 1991 Traversing large pieces of linearity in algorithms that solve equations by following piecewise-linear paths. Zbl 0441.90111Todd, Michael J. 10 1980 An implementation of the simplex method for linear programming problems with variable upper bounds. Zbl 0477.90039Todd, Michael J. 10 1982 Sensitivity analysis in linear programming and semidefinite programming using interior-point methods. Zbl 1017.90110Yıldırım, E. Alper; Todd, Michael J. 9 2001 On Anstreicher’s combined phase I-phase II projective algorithm for linear programming. Zbl 0773.90049Todd, Michael J. 9 1992 Characterizations, bounds, and probabilistic analysis of two complexity measures for linear programming problems. Zbl 0978.90069Todd, Michael J.; Tunçel, Levent; Ye, Yinyu 9 2001 A generalized complementary pivoting algorithm. Zbl 0285.90053Todd, Michael J. 9 1974 A variable-dimension simplicial algorithm for antipodal fixed-point theorems. Zbl 0456.65024Todd, Michael J.; Wright, Alden H. 8 1980 A low complexity interior-point algorithm for linear programming. Zbl 0811.90070Todd, Michael J. 7 1992 Interior-point algorithms for semi-infinite programming. Zbl 0831.90114Todd, Michael J. 7 1994 A lower bound on the number of iterations of long-step primal-dual linear programming algorithms. Zbl 0848.90092Todd, Michael J.; Ye, Yinyu 7 1996 A note on computing equilibria in economies with activity analysis models of production. Zbl 0432.90014Todd, Michael J. 7 1979 Optimization. Zbl 0688.90034 6 1989 The ellipsoid method generates dual variables. Zbl 0582.90070Burrell, Bruce P.; Todd, Michael J. 6 1985 New results on the average behavior of simplex algorithms. Zbl 0545.90066Adler, Ilan; Megiddo, Nimrod; Todd, Michael J. 6 1984 Potential-reduction methods in mathematical programming. Zbl 0881.90097Todd, Michael J. 6 1997 Optimal conditioning and convergence in rank one quasi-Newton updates. Zbl 0638.65041Ip, Chi Ming; Todd, Michael J. 6 1988 Union Jack triangulations. Zbl 0424.90084Todd, Michael J. 6 1977 Minimum-volume ellipsoids. Theory and algorithms. Zbl 1360.90006Todd, Michael J. 6 2016 An interior-point approach to sensitivity analysis in degenerate linear programs. Zbl 1008.90064Yildirim, E. Alper; Todd, Michael J. 5 2002 On the computational complexity of piecewise-linear homotopy algorithms. Zbl 0509.90071Todd, Michael J. 5 1982 Large-scale linear programming: Geometry, working bases and factorizations. Zbl 0516.90051Todd, Michael J. 5 1983 Exploiting structure in piecewise-linear homotopy algorithms for solving equations. Zbl 0433.90088Todd, Michael J. 5 1980 Path-following methods. Zbl 0957.90523Monteiro, Renato; Todd, Michael 5 2000 Combining phase I and phase II in a potential reduction algorithm for linear programming. Zbl 0777.90030Todd, Michael J. 5 1993 A modified Frank–Wolfe algorithm for computing minimum-area enclosing ellipsoidal cylinders: theory and algorithms. Zbl 1266.65035Damla Ahipaşaoğlu, S.; Todd, Michael J. 4 2013 The effects of degeneracy and null and unbounded variables on variants of Karmarkar’s linear programming algorithm. Zbl 0726.90054Todd, Michael J. 4 1990 Approximate Farkas lemmas and stopping rules for iterative infeasible-point algorithms for linear programming. Zbl 0949.90060Todd, Michael J.; Ye, Yinyu 4 1998 Solving the generalized market area problem. Zbl 0492.90041Todd, Michael J. 4 1978 Quasi-Newton updates in abstract vector spaces. Zbl 0574.65044Todd, Michael J. 4 1984 Symmetry and positive definiteness in oriented matroids. Zbl 0649.05023Morris, Walter D. jun.; Todd, Michael J. 4 1988 Exploiting special structure in Karmarkar’s linear programming algorithm. Zbl 0649.90070Todd, Michael J. 4 1988 A variant of Karmarkar’s linear programming algorithm for problems with some unrestricted variables. Zbl 0667.65048Mitchell, John E.; Todd, Michael J. 4 1989 On the interplay among entropy, variable metrics and potential functions in interior-point algorithms. Zbl 0880.90103Tunçel, Levent; Todd, Michael J. 4 1997 A combinatorial generalization of polytopes. Zbl 0295.05007Todd, Michael J. 4 1976 Characterizing binary simplicial matroids. Zbl 0337.05021Todd, Michael J. 4 1976 Todd’s low-complexity algorithm is a predictor-corrector path-following method. Zbl 0768.90055Todd, M. J.; Vial, J.-P. 3 1992 On combined phase 1-phase 2 projective methods for linear programming. Zbl 0767.90048Todd, Michael J.; Wang, Yufei 3 1993 Detecting infeasibility in infeasible-interior-point methods for optimization. Zbl 1142.90499Todd, Michael J. 3 2004 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 3 1983 Optimal dissection of simplices. Zbl 0384.52008Todd, Michael J. 3 1978 A quadratically-convergent fixed-point algorithm for economic equilibria and linearly constrained optimization. Zbl 0429.90081Todd, Michael J. 3 1980 Global and local convergence and monotonicity results for a recent variable-dimension simplicial algorithm. Zbl 0449.65021Todd, Michael J. 3 1980 Asymptotic behavior of interior-point methods: A view from semi-infinite programming. Zbl 0857.90085Tunçel, Levent; Todd, Michael J. 3 1996 An efficient simplicial algorithm for computing a zero of a convex union of smooth functions. Zbl 0493.90074Awoniyi, Samuel A.; Todd, Michael J. 2 1983 An introduction to piecewise-linear homotopy algorithms for solving systems of equations. Zbl 0495.65020Todd, Michael J. 2 1982 Approximate labelling for simplicial algorithms and two classes of special subsets of the sphere. Zbl 0503.90082Todd, Michael J. 2 1981 A new triangulation for simplicial algorithms. Zbl 0778.65038Todd, Michael J.; Tunçel, Levent 2 1993 An \(O(n^ 3L)\) adaptive path following algorithm for a linear complementarity problem. Zbl 0745.90070Mizuno, Shinji; Todd, Michael J. 2 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 2 1990 A lower bound on the number of iterations of an interior-point algorithm for linear programming. Zbl 0815.65081Todd, M. J. 2 1994 Minimum-volume ellipsoids. Theory and algorithms. Zbl 1360.90006Todd, Michael J. 6 2016 Computation, multiplicity, and comparative statics of Cournot equilibria in integers. Zbl 1347.91189Todd, Michael J. 2 2016 An improved Kalai-Kleitman bound for the diameter of a polyhedron. Zbl 1316.52021Todd, Michael J. 13 2014 Optimization of demand response through peak shaving. Zbl 1408.90181Zakeri, G.; Craigie, D.; Philpott, A.; Todd, M. 1 2014 A modified Frank–Wolfe algorithm for computing minimum-area enclosing ellipsoidal cylinders: theory and algorithms. Zbl 1266.65035Damla Ahipaşaoğlu, S.; Todd, Michael J. 4 2013 On the implementation and usage of SDPT3 – a Matlab software package for semidefinite-quadratic-linear programming, version 4.0. Zbl 1334.90117Toh, Kim-Chuan; Todd, Michael J.; Tütüncü, Reha H. 50 2012 A robust robust optimization result. Zbl 1242.90249Gancarova, Martina; Todd, Michael J. 2 2012 Book review of: George B. Dantzig, The basic George B. Dantzig. Zbl 1292.00042Todd, Michael J. 1 2011 Weighted distance weighted discrimination and its asymptotic properties. Zbl 1397.62227Qiao, Xingye; Zhang, Hao Helen; Liu, Yufeng; Todd, Michael J.; Marron, J. S. 22 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 1 2009 Largest dual ellipsoids inscribed in dual cones. Zbl 1165.90025Todd, M. J. 1 2009 Linear convergence of a modified Frank-Wolfe algorithm for computing minimum-volume enclosing ellipsoids. Zbl 1146.90047Ahipasaoglu, S. Damla; Sun, Peng; Todd, Michael J. 24 2008 Interior-point methods for optimization. Zbl 1160.65027Nemirovski, Arkadi S.; Todd, Michael J. 18 2008 Dual versus primal-dual interior-point methods for linear and conic programming. Zbl 1163.90797Todd, M. J. 1 2008 Distance-weighted discrimination. Zbl 1332.62213Marron, J. S.; Todd, Michael J.; Ahn, Jeongyoun 46 2007 On Khachiyan’s algorithm for the computation of minimum-volume enclosing ellipsoids. Zbl 1151.90516Todd, Michael J.; Yıldırım, E. Alper 30 2007 Inexact primal-dual path-following algorithms for a special class of convex quadratic SDP and related problems. Zbl 1136.90026Toh, K. C.; Tütüncü, R. H.; Todd, M. J. 18 2007 Two new proofs of Afriat’s theorem. Zbl 1084.91032Fostel, A.; Scarf, H. E.; Todd, M. J. 25 2004 Detecting infeasibility in infeasible-interior-point methods for optimization. Zbl 1142.90499Todd, Michael J. 3 2004 Solving semidefinite-quadratic-linear programs using SDPT3. Zbl 1030.90082Tütüncü, R. H.; Toh, K. C.; Todd, M. J. 233 2003 On the Riemannian geometry defined by self-concordant barriers and interior-point methods. Zbl 1049.90127Nesterov, Yu. E.; Todd, M. J. 50 2002 The many facets of linear programming. Zbl 1030.90051Todd, Michael J. 28 2002 An interior-point approach to sensitivity analysis in degenerate linear programs. Zbl 1008.90064Yildirim, E. Alper; Todd, Michael J. 5 2002 Semidefinite optimization. Zbl 1105.65334Todd, M. J. 165 2001 Sensitivity analysis in linear programming and semidefinite programming using interior-point methods. Zbl 1017.90110Yıldırım, E. Alper; Todd, Michael J. 9 2001 Characterizations, bounds, and probabilistic analysis of two complexity measures for linear programming problems. Zbl 0978.90069Todd, Michael J.; Tunçel, Levent; Ye, Yinyu 9 2001 On two homogeneous self-dual approaches to linear programming and its extensions. Zbl 1098.90530Mizuno, Shinji; Todd, Michael J. 1 2001 Path-following methods. Zbl 0957.90523Monteiro, Renato; Todd, Michael 5 2000 Least-change quasi-Newton updates for equality-constrained optimization. Zbl 0970.90120Wagner, Michael; Todd, Michael J. 1 2000 SDPT3 – a MATLAB software package for semidefinite programming, version 1. 3. Zbl 0997.90060Toh, K. C.; Todd, M. J.; Tütüncü, R. H. 305 1999 A study of search directions in primal-dual interior-point methods for semidefinite programming. Zbl 0971.90109Todd, M. J. 36 1999 Infeasible-start primal-dual methods and infeasibility detectors for nonlinear programming problems. Zbl 0971.90061Nesterov, Yu.; Todd, M. J.; Ye, Y. 27 1999 Primal-dual interior-point methods for self-scaled cones. Zbl 0922.90110Nesterov, Yu. E.; Todd, M. J. 192 1998 On the Nesterov-Todd direction in semidefinite programming. Zbl 0913.90217Todd, M. J.; Toh, K. C.; Tütüncü, R. H. 83 1998 Approximate Farkas lemmas and stopping rules for iterative infeasible-point algorithms for linear programming. Zbl 0949.90060Todd, Michael J.; Ye, Yinyu 4 1998 Erratum: Probabilistic models for linear programming. Zbl 0977.90032Todd, M. J. 1 1998 Self-scaled barriers and interior-point methods for convex programming. Zbl 0871.90064Nesterov, Yu. E.; Todd, M. J. 201 1997 Potential-reduction methods in mathematical programming. Zbl 0881.90097Todd, Michael J. 6 1997 On the interplay among entropy, variable metrics and potential functions in interior-point algorithms. Zbl 0880.90103Tunçel, Levent; Todd, Michael J. 4 1997 Mathematical programming. Zbl 0904.90155Todd, Michael J. 1 1997 A lower bound on the number of iterations of long-step primal-dual linear programming algorithms. Zbl 0848.90092Todd, Michael J.; Ye, Yinyu 7 1996 Asymptotic behavior of interior-point methods: A view from semi-infinite programming. Zbl 0857.90085Tunçel, Levent; Todd, Michael J. 3 1996 Solving LP problems via weighted centers. Zbl 0872.65049Liao, Aiping; Todd, Michael J. 1 1996 Infeasible-interior-point primal-dual potential-reduction algorithms for linear programming. Zbl 0832.90076Mizuno, Shinji; Kojima, Masakazu; Todd, Michael J. 25 1995 A surface of analytic centers and primal-dual infeasible-interior-point algorithms for linear programming. Zbl 0834.90088Mizuno, Shinji; Todd, Michael J.; Ye, Yinyu 13 1995 Reducing horizontal linear complementarity problems. Zbl 0835.90106Tütüncü, Reha H.; Todd, Michael J. 11 1995 Barrier functions and interior-point algorithms for linear programming with zero-, one, or two-sided bounds on the variables. Zbl 0837.90083Freund, Robert M.; Todd, Michael J. 2 1995 An \(O(\sqrt{n} L)\)-iteration homogeneous and self-dual linear programming algorithm. Zbl 0799.90087Ye, Yinyu; Todd, Michael J.; Mizuno, Shinji 90 1994 Interior-point algorithms for semi-infinite programming. Zbl 0831.90114Todd, Michael J. 7 1994 A lower bound on the number of iterations of an interior-point algorithm for linear programming. Zbl 0815.65081Todd, M. J. 2 1994 Theory and practice for interior-point methods. Zbl 0800.90700Todd, Michael J. 2 1994 Monotonicity of primal and dual objective values in primal-dual interior- point algorithms. Zbl 0827.90108Mizuno, Shinji; Todd, Michael J.; Tunçel, Levent 1 1994 Analysis of interior-point methods for linear programming problems with variable upper bounds. Zbl 0823.90086Todd, Michael J. 1 1994 Scaling, shifting and weighting in interior-point methods. Zbl 0924.90112Todd, Michael J. 1 1994 On adaptive-step primal-dual interior-point algorithms for linear programming. Zbl 0810.90091Mizuno, Shinji; Todd, Michael J.; Ye, Yinyu 150 1993 On the complexity of approximating the maximal inscribed ellipsoid for a polytope. Zbl 0792.90088Khachiyan, Leonid G.; Todd, Michael J. 33 1993 Combining phase I and phase II in a potential reduction algorithm for linear programming. Zbl 0777.90030Todd, Michael J. 5 1993 On combined phase 1-phase 2 projective methods for linear programming. Zbl 0767.90048Todd, Michael J.; Wang, Yufei 3 1993 A new triangulation for simplicial algorithms. Zbl 0778.65038Todd, Michael J.; Tunçel, Levent 2 1993 Solving combinatorial optimization problems using Karmarkar’s algorithm. Zbl 0763.90074Mitchell, John E.; Todd, Michael J. 22 1992 An \(O(\sqrt n L)\)-iteration large-step primal-dual affine algorithm for linear programming. Zbl 0783.90071Gonzaga, C. C.; Todd, M. J. 12 1992 On Anstreicher’s combined phase I-phase II projective algorithm for linear programming. Zbl 0773.90049Todd, Michael J. 9 1992 A low complexity interior-point algorithm for linear programming. Zbl 0811.90070Todd, Michael J. 7 1992 Todd’s low-complexity algorithm is a predictor-corrector path-following method. Zbl 0768.90055Todd, M. J.; Vial, J.-P. 3 1992 Probabilistic models for linear programming. Zbl 0751.90056Todd, Michael J. 10 1991 An \(O(n^ 3L)\) adaptive path following algorithm for a linear complementarity problem. Zbl 0745.90070Mizuno, Shinji; Todd, Michael J. 2 1991 The affine-scaling direction for linear programming is a limit of projective-scaling directions. Zbl 0729.65041Todd, Michael J. 1 1991 A centered projective algorithm for linear programming. Zbl 0722.90044Todd, Michael J.; Ye, Yinyu 63 1990 Convex resource allocation problems on directed acyclic graphs: Duality, complexity, special cases, and extensions. Zbl 0717.90080Monma, Clyde L.; Schrijver, Alexander; Todd, Michael J.; Wei, Victor K. 37 1990 A Dantzig-Wolfe-like variant of Karmarkar’s interior-point linear programming algorithm. Zbl 0724.90037Todd, Michael J. 14 1990 Containing and shrinking ellipsoids in the path-following algorithm. Zbl 0746.90049Ye, Yinyu; Todd, Michael J. 14 1990 The effects of degeneracy and null and unbounded variables on variants of Karmarkar’s linear programming algorithm. Zbl 0726.90054Todd, Michael J. 4 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 2 1990 Recent developments and new directions in linear programming. Zbl 0683.90044Todd, Michael J. 14 1989 On convergence properties of algorithms for unconstrained minimization. Zbl 0686.65032Todd, Michael J. 13 1989 Optimization. Zbl 0688.90034 6 1989 A variant of Karmarkar’s linear programming algorithm for problems with some unrestricted variables. Zbl 0667.65048Mitchell, John E.; Todd, Michael J. 4 1989 Improved bounds and containing ellipsoids in Karmarkar’s linear programming algorithm. Zbl 0665.90059Todd, Michael J. 18 1988 Optimal conditioning and convergence in rank one quasi-Newton updates. Zbl 0638.65041Ip, Chi Ming; Todd, Michael J. 6 1988 Symmetry and positive definiteness in oriented matroids. Zbl 0649.05023Morris, Walter D. jun.; Todd, Michael J. 4 1988 Exploiting special structure in Karmarkar’s linear programming algorithm. Zbl 0649.90070Todd, Michael J. 4 1988 Polynomial algorithms for linear programming. Zbl 0651.90046Todd, Michael J. 1 1988 An extension of Karmarkar’s algorithm for linear programming using dual variables. Zbl 0621.90048Todd, Michael J.; Burrell, Bruce P. 75 1986 Polynomial expected behavior of a pivoting algorithm for linear complementarity and linear programming problems. Zbl 0613.90094Todd, Michael J. 17 1986 The symmetric rank-one quasi-Newton method is a space-dilation subgradient algorithm. Zbl 0604.90113Todd, Michael J. 1 1986 Linear quadratic programming in oriented matroids. Zbl 0555.05026Todd, Michael J. 14 1985 The ellipsoid method generates dual variables. Zbl 0582.90070Burrell, Bruce P.; Todd, Michael J. 6 1985 “Fat” triangulations, or solving certain nonconvex matrix optimization problems. Zbl 0588.90074Todd, Michael J. 1 1985 Complementarity in oriented matroids. Zbl 0556.05016Todd, Michael J. 14 1984 New results on the average behavior of simplex algorithms. Zbl 0545.90066Adler, Ilan; Megiddo, Nimrod; Todd, Michael J. 6 1984 Quasi-Newton updates in abstract vector spaces. Zbl 0574.65044Todd, Michael J. 4 1984 J’: A new triangulation of \({\mathbb{R}}^ n\). Zbl 0542.65027Todd, Michael J. 1 1984 Large-scale linear programming: Geometry, working bases and factorizations. Zbl 0516.90051Todd, Michael J. 5 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 3 1983 An efficient simplicial algorithm for computing a zero of a convex union of smooth functions. Zbl 0493.90074Awoniyi, Samuel A.; Todd, Michael J. 2 1983 Piecewise-linear homotopy algorithms for sparse systems of nonlinear equations. Zbl 0508.65019Todd, Michael J. 2 1983 Modifications and implementation of the ellipsoid algorithm for linear programming. Zbl 0477.90038Goldfarb, Donald; Todd, Michael J. 14 1982 On minimum volume ellipsoids containing part of a given ellipsoid. Zbl 0503.90065Todd, Michael J. 10 1982 An implementation of the simplex method for linear programming problems with variable upper bounds. Zbl 0477.90039Todd, Michael J. 10 1982 On the computational complexity of piecewise-linear homotopy algorithms. Zbl 0509.90071Todd, Michael J. 5 1982 ...and 28 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 2,399 Authors 48 Todd, Michael J. 43 Kheirfam, Behrouz 43 Ye, Yinyu 36 Terlaky, Tamás 33 Kojima, Masakazu 27 Toh, Kim Chuan 25 Roos, Cornelis 24 Liu, Hongwei 21 Wang, Guoqiang 18 Potra, Florian-Alexandru 17 Bai, Yanqin 16 Boyd, Stephen Poythress 16 Ferreira, Orizon Pereira 16 Mizuno, Shinji 16 Shabtay, Dvir 15 Zhang, Shuzhong 14 Darvay, Zsolt 14 Tsuchiya, Takashi 14 Tunçel, Levent 14 Van der Laan, Gerard 13 Anstreicher, Kurt M. 13 Freund, Robert M. 13 Monteiro, Renato D. C. 13 Oliveira, Paulo Roberto 12 Kim, Sunyoung 12 Liu, Changhe 12 Sun, Defeng 12 Vial, Jean-Philippe 12 Yang, Ximei 12 Zangiabadi, Maryam 11 Goldfarb, Donald 11 Marron, James Stephen 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 Gondzio, Jacek 10 Lim, Yongdo 9 Aoshima, Makoto 9 Dang, Chuangyin 9 Jarre, Florian 9 Mansouri, Hossein 9 Muramatsu, Masakazu 9 Nemirovski, Arkadi S. 9 Peña, Javier F. 9 Sun, Jie 9 Yamashita, Makoto 9 Yang, Zaifu 9 Yata, Kazuyoshi 8 Asadi, Soodabeh 8 Gonzaga, Clovis C. 8 Huang, Zheng-Hai 8 Peng, Jiming 8 Povh, Janez 8 Salahi, Maziar 8 Tran Dinh Quoc 7 de Klerk, Etienne 7 Fang, Liang 7 Farhood, Mazen 7 Gillis, Nicolas 7 Kanno, Yoshihiro 7 Klep, Igor 7 Lasserre, Jean-Bernard 7 Lesaja, Goran 7 Luo, Hezhi 7 Megiddo, Nimrod 7 Qi, Houduo 7 Qi, Liqun 7 Rendl, Franz 7 Steiner, George 7 Vandenberghe, Lieven 7 Vavasis, Stephen A. 7 Waki, Hayato 7 Wright, Stephen J. 7 Yamamoto, Yoshitsugu 7 Yang, Yaguang 7 Yoshise, Akiko 7 Zhang, Lei-Hong 7 Zhang, Yinkui 6 Açıkmeşe, Behçet 6 Chandrasekaran, Venkat 6 da Cruz Neto, João Xavier 6 D’Apuzzo, Marco 6 den Hertog, Dick 6 Eaves, B. Curtis 6 Faybusovich, Leonid E. 6 Fukushima, Masao 6 Goulart, Paul J. 6 Güler, Osman 6 Illés, Tibor 6 Kaspi, Moshe 6 Mahdavi-Amiri, Nezam 6 Mehrotra, Sanjay 6 Nesterov, Yurii 6 Rigó, Petra Renáta 6 Santos, Francisco 6 Shi, Zhenjun ...and 2,299 more Authors all top 5 Cited in 295 Serials 225 Mathematical Programming. Series A. Series B 116 Journal of Optimization Theory and Applications 93 Computational Optimization and Applications 76 Optimization Methods & Software 65 European Journal of Operational Research 61 Mathematical Programming 50 Linear Algebra and its Applications 44 Operations Research Letters 43 SIAM Journal on Optimization 42 Annals of Operations Research 38 Automatica 38 Optimization 35 Journal of Global Optimization 31 Optimization Letters 29 International Journal of Control 27 Applied Mathematics and Computation 26 Computers & Operations Research 24 Numerical Algorithms 23 Discrete Applied Mathematics 20 Journal of Mathematical Analysis and Applications 19 Journal of Computational and Applied Mathematics 18 Mathematical Programming Computation 15 Optimization and Engineering 14 Algorithmica 13 Discrete Mathematics 13 Numerical Functional Analysis and Optimization 13 Acta Mathematicae Applicatae Sinica. 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Series A: Theory and Methods 5 Operations Research 5 Automation and Remote Control 5 Pattern Recognition 5 INFORMS Journal on Computing 5 Journal of Scheduling 5 Acta Mathematica Sinica. English Series 5 Journal of Machine Learning Research (JMLR) 5 4OR 5 Electronic Journal of Statistics 5 Asian Journal of Control 4 International Journal for Numerical Methods in Engineering 4 Journal of the American Statistical Association 4 Journal of Computer and System Sciences 4 SIAM Journal on Algebraic and Discrete Methods 4 Statistical Science 4 Mathematical and Computer Modelling 4 SIAM Journal on Discrete Mathematics 4 Science in China. Series A 4 Japan Journal of Industrial and Applied Mathematics 4 Applied Mathematical Modelling 4 Journal of Mathematical Imaging and Vision 4 Applied and Computational Harmonic Analysis 4 Numerical Linear Algebra with Applications 4 New Journal of Physics 4 The ANZIAM Journal 4 Discrete Optimization 4 The Annals of Applied Statistics 4 SIAM Journal on Imaging Sciences 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 Annals of the Institute of Statistical Mathematics ...and 195 more Serials all top 5 Cited in 54 Fields 1,529 Operations research, mathematical programming (90-XX) 440 Numerical analysis (65-XX) 153 Computer science (68-XX) 145 Systems theory; control (93-XX) 142 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 113 Statistics (62-XX) 112 Calculus of variations and optimal control; optimization (49-XX) 81 Convex and discrete geometry (52-XX) 78 Linear and multilinear algebra; matrix theory (15-XX) 71 Combinatorics (05-XX) 40 Operator theory (47-XX) 37 General topology (54-XX) 23 Algebraic topology (55-XX) 22 Biology and other natural sciences (92-XX) 21 Information and communication theory, circuits (94-XX) 20 Mechanics of deformable solids (74-XX) 17 Probability theory and stochastic processes (60-XX) 15 Algebraic geometry (14-XX) 14 Ordinary differential equations (34-XX) 12 Real functions (26-XX) 11 Partial differential equations (35-XX) 11 Approximations and expansions (41-XX) 11 Global analysis, analysis on manifolds (58-XX) 10 Nonassociative rings and algebras (17-XX) 10 Functional analysis (46-XX) 10 Differential geometry (53-XX) 9 Commutative algebra (13-XX) 9 Manifolds and cell complexes (57-XX) 8 Dynamical systems and ergodic theory (37-XX) 7 Geometry (51-XX) 7 Quantum theory (81-XX) 6 Mathematical logic and foundations (03-XX) 6 Number theory (11-XX) 6 Mechanics of particles and systems (70-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 History and biography (01-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 Difference and functional equations (39-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) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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