Todd, Michael J. 1947
Overview
Works:  98 works in 227 publications in 5 languages and 1,862 library holdings 

Genres:  Conference papers and proceedings 
Roles:  Author, Editor, Honoree, Other 
Publication Timeline
.
Most widely held works about
Michael J Todd
Most widely held works by
Michael J Todd
Optimization by
George L Nemhauser(
Book
)
20 editions published between 1989 and 1998 in English and Spanish and held by 451 WorldCat member libraries worldwide
A view of unconstrained optimization (J.E. Dennis Jr. and R.B. Schanbel). Linear programming (D. Goldfarb and M.J. Todd). Constrained nonlinear programming ((P.E. Gill, W. Myrray, M.A. Saunders and M.H. Wright). Network flows (R.K. Ahuja, T.L. Magnanti and J.B. Orlin). Polyhedral combinatorics (W.R.Pulleyblank). Integer programming (G.L.Nemhauser and L.A. Wolsey). Nondifferentiable optimization (C. Lemaréchal). Stochastic programming (R.JB. Wets). Global optimization (A.H.G. Rinnoy Kan and G.T. Timmer). Multiple criteria decision making: five basic concepts (P.L.Yu)
20 editions published between 1989 and 1998 in English and Spanish and held by 451 WorldCat member libraries worldwide
A view of unconstrained optimization (J.E. Dennis Jr. and R.B. Schanbel). Linear programming (D. Goldfarb and M.J. Todd). Constrained nonlinear programming ((P.E. Gill, W. Myrray, M.A. Saunders and M.H. Wright). Network flows (R.K. Ahuja, T.L. Magnanti and J.B. Orlin). Polyhedral combinatorics (W.R.Pulleyblank). Integer programming (G.L.Nemhauser and L.A. Wolsey). Nondifferentiable optimization (C. Lemaréchal). Stochastic programming (R.JB. Wets). Global optimization (A.H.G. Rinnoy Kan and G.T. Timmer). Multiple criteria decision making: five basic concepts (P.L.Yu)
The computation of fixed points and applications by
Michael J Todd(
Book
)
26 editions published between 1976 and 1983 in 3 languages and held by 391 WorldCat member libraries worldwide
Fixedpoint algorithms have diverse applications in economics, optimization, game theory and the numerical solution of boundaryvalue problems. Since Scarf's pioneering work [56,57] on obtaining approximate fixed points of continuous mappings, a great deal of research has been done in extending the applicability and improving the efficiency of fixedpoint methods. Much of this work is available only in research papers, although Scarf's book [58] gives a remarkably clear exposition of the power of fixedpoint methods. However, the algorithms described by Scarf have been super~eded by the more sophisticated restart and homotopy techniques of Merrill [~8,~9] and Eaves and Saigal [1~,16]. To understand the more efficient algorithms one must become familiar with the notions of triangulation and simplicial approxi tion, whereas Scarf stresses the concept of primitive set. These notes are intended to introduce to a wider audience the most recent fixedpoint methods and their applications. Our approach is therefore via triangu tions. For this reason, Scarf is cited less in this manuscript than his contri tions would otherwise warrant. We have also confined our treatment of applications to the computation of economic equilibria and the solution of optimization problems. Hansen and Koopmans [28] apply fixedpoint methods to the computation of an invariant optimal capital stock in an economic growth model. Applications to game theory are discussed in Scarf [56,58], Shapley [59], and Garcia, Lemke and Luethi [24]. Allgower [1] and Jeppson [31] use fixedpoint algorithms to find many solutions to boundaryvalue problems
26 editions published between 1976 and 1983 in 3 languages and held by 391 WorldCat member libraries worldwide
Fixedpoint algorithms have diverse applications in economics, optimization, game theory and the numerical solution of boundaryvalue problems. Since Scarf's pioneering work [56,57] on obtaining approximate fixed points of continuous mappings, a great deal of research has been done in extending the applicability and improving the efficiency of fixedpoint methods. Much of this work is available only in research papers, although Scarf's book [58] gives a remarkably clear exposition of the power of fixedpoint methods. However, the algorithms described by Scarf have been super~eded by the more sophisticated restart and homotopy techniques of Merrill [~8,~9] and Eaves and Saigal [1~,16]. To understand the more efficient algorithms one must become familiar with the notions of triangulation and simplicial approxi tion, whereas Scarf stresses the concept of primitive set. These notes are intended to introduce to a wider audience the most recent fixedpoint methods and their applications. Our approach is therefore via triangu tions. For this reason, Scarf is cited less in this manuscript than his contri tions would otherwise warrant. We have also confined our treatment of applications to the computation of economic equilibria and the solution of optimization problems. Hansen and Koopmans [28] apply fixedpoint methods to the computation of an invariant optimal capital stock in an economic growth model. Applications to game theory are discussed in Scarf [56,58], Shapley [59], and Garcia, Lemke and Luethi [24]. Allgower [1] and Jeppson [31] use fixedpoint algorithms to find many solutions to boundaryvalue problems
Mathematical developments arising from linear programming : proceedings of a joint summer research conference held at Bowdoin
College, June 25July 1, 1988 by
Jeffrey C Lagarias(
Book
)
16 editions published between 1990 and 1991 in English and held by 248 WorldCat member libraries worldwide
16 editions published between 1990 and 1991 in English and held by 248 WorldCat member libraries worldwide
Foundations of computational mathematics, Hong Kong 2008 by Foundations of Computational Mathematics (Conference)(
Book
)
11 editions published in 2009 in English and held by 191 WorldCat member libraries worldwide
This volume is a collection of articles based on the plenary talks presented at the 2008 Society for the Foundations of Computational Mathematics meeting in Hong Kong. The talks were given by some of the foremost world authorities in computational mathematics. The topics covered reflect the breadth of research within the area as well as the richness and fertility of interactions between seemingly unrelated branches of pure and applied mathematics. As a result, this volume will be of interest to researchers in the field of computational mathematics and also to nonexperts who wish to gain some insight into the state of the art in this active and significant field
11 editions published in 2009 in English and held by 191 WorldCat member libraries worldwide
This volume is a collection of articles based on the plenary talks presented at the 2008 Society for the Foundations of Computational Mathematics meeting in Hong Kong. The talks were given by some of the foremost world authorities in computational mathematics. The topics covered reflect the breadth of research within the area as well as the richness and fertility of interactions between seemingly unrelated branches of pure and applied mathematics. As a result, this volume will be of interest to researchers in the field of computational mathematics and also to nonexperts who wish to gain some insight into the state of the art in this active and significant field
Minimumvolume ellipsoids : theory and algorithms by
Michael J Todd(
Book
)
6 editions published in 2016 in English and held by 41 WorldCat member libraries worldwide
This book, the first on these topics, addresses the problem of finding an ellipsoid to represent a large set of points in highdimensional space, which has applications in computational geometry, data representations, and optimal design in statistics. The book covers the formulation of this and related problems, theoretical properties of their optimal solutions, and algorithms for their solution. Due to the high dimensionality of these problems, firstorder methods that require minimal computational work at each iteration are attractive. While algorithms of this kind have been discovered and rediscovered over the past fifty years, their computational complexities and convergence rates have only recently been investigated. The optimization problems in the book have the entries of a symmetric matrix as their variables, so the author's treatment also gives an introduction to recent work in matrix optimization. This book provides historical perspective on the problems studied by optimizers, statisticians, and geometric functional analysts; demonstrates the huge computational savings possible by exploiting simple updates for the determinant and the inverse after a rankone update, and highlights the difficulties in algorithms when related problems are studied that do not allow simple updates at each iteration; and gives rigorous analyses of the proposed algorithms, MATLAB codes, and computational results
6 editions published in 2016 in English and held by 41 WorldCat member libraries worldwide
This book, the first on these topics, addresses the problem of finding an ellipsoid to represent a large set of points in highdimensional space, which has applications in computational geometry, data representations, and optimal design in statistics. The book covers the formulation of this and related problems, theoretical properties of their optimal solutions, and algorithms for their solution. Due to the high dimensionality of these problems, firstorder methods that require minimal computational work at each iteration are attractive. While algorithms of this kind have been discovered and rediscovered over the past fifty years, their computational complexities and convergence rates have only recently been investigated. The optimization problems in the book have the entries of a symmetric matrix as their variables, so the author's treatment also gives an introduction to recent work in matrix optimization. This book provides historical perspective on the problems studied by optimizers, statisticians, and geometric functional analysts; demonstrates the huge computational savings possible by exploiting simple updates for the determinant and the inverse after a rankone update, and highlights the difficulties in algorithms when related problems are studied that do not allow simple updates at each iteration; and gives rigorous analyses of the proposed algorithms, MATLAB codes, and computational results
Report on Intensive Foster Care Scheme, December 1979February 1982 by
Jane Thomson(
Book
)
1 edition published in 1982 in English and held by 14 WorldCat member libraries worldwide
1 edition published in 1982 in English and held by 14 WorldCat member libraries worldwide
Musiek vir 'n fluit by
Rene Deetlefs(
Book
)
2 editions published in 1985 in Afrikaans and held by 7 WorldCat member libraries worldwide
2 editions published in 1985 in Afrikaans and held by 7 WorldCat member libraries worldwide
Primaldual interiorpoint methods for selfscaled cones by
I︠U︡. E Nesterov(
Book
)
4 editions published in 1995 in English and held by 7 WorldCat member libraries worldwide
4 editions published in 1995 in English and held by 7 WorldCat member libraries worldwide
New successful English : grade 2: learner's book by
D. J Botha(
Book
)
2 editions published between 1997 and 1998 in English and held by 7 WorldCat member libraries worldwide
2 editions published between 1997 and 1998 in English and held by 7 WorldCat member libraries worldwide
Modifications and implementation of the ShorKhachian algorithm for linear programming by
Donald Goldfarb(
Book
)
6 editions published in 1980 in English and held by 6 WorldCat member libraries worldwide
We give some modifications of the recent ShorKhachian algorithm for linear programming and describe a numerically stable implementation. We are concerned with practical problems where usersupplied bounds can usually be provided. Our implementation allows constraint dropping and updates bounds on the optimal value, and should be able to terminate with an indication of infeasibility or with a provably good feasible solution in a moderate number of iterations
6 editions published in 1980 in English and held by 6 WorldCat member libraries worldwide
We give some modifications of the recent ShorKhachian algorithm for linear programming and describe a numerically stable implementation. We are concerned with practical problems where usersupplied bounds can usually be provided. Our implementation allows constraint dropping and updates bounds on the optimal value, and should be able to terminate with an indication of infeasibility or with a provably good feasible solution in a moderate number of iterations
Primaldual methods and infeasibility detectors for nonlinear programming problems by
I︠U︡. E Nesterov(
Book
)
4 editions published in 1996 in English and held by 6 WorldCat member libraries worldwide
4 editions published in 1996 in English and held by 6 WorldCat member libraries worldwide
Selfscaled cones and interiorpoint methods in nonlinear programming by
Jurij Evgenʹevič Nesterov(
Book
)
5 editions published in 1994 in English and held by 5 WorldCat member libraries worldwide
5 editions published in 1994 in English and held by 5 WorldCat member libraries worldwide
Exploiting structure in fixedpoint computation by
Michael J Todd(
Book
)
4 editions published in 1978 in English and held by 5 WorldCat member libraries worldwide
We consider the recent algorithms for computing fixed points of zeros of continuous functions from R to the nth power to itself that are based on tracing piecewiselinear paths in triangulations. We investigate the possible savings that arise when these fixedpoint algorithms with their usual triangulations are applied to computing zeros of functions f with special structure: f is either linear in certain variables, separable, or has Jacobian with small bandwidth. Each of these structures leads to a property we call modularity; the algorithmic path within a simplex can be continued into an adjacent simplex without a function evaluation or linear programming pivot. Modularity also arises without any special structure on f from the linearity of the function that is deformed to f
4 editions published in 1978 in English and held by 5 WorldCat member libraries worldwide
We consider the recent algorithms for computing fixed points of zeros of continuous functions from R to the nth power to itself that are based on tracing piecewiselinear paths in triangulations. We investigate the possible savings that arise when these fixedpoint algorithms with their usual triangulations are applied to computing zeros of functions f with special structure: f is either linear in certain variables, separable, or has Jacobian with small bandwidth. Each of these structures leads to a property we call modularity; the algorithmic path within a simplex can be continued into an adjacent simplex without a function evaluation or linear programming pivot. Modularity also arises without any special structure on f from the linearity of the function that is deformed to f
Image data compression by
Michael J Todd(
Book
)
3 editions published in 1988 in English and held by 5 WorldCat member libraries worldwide
3 editions published in 1988 in English and held by 5 WorldCat member libraries worldwide
The ellipsoid method : a survey by Robert G Bland(
Book
)
3 editions published in 1980 in English and held by 4 WorldCat member libraries worldwide
IN February 1979 a note by L.G. Khachiyan indicated how an ellipsoid method for linear programming can be implemented in polynomial time. This result has caused great excitement and stimulated a flood of technical papers. Ordinarily there would be no need for a survey of work so recent. The current circumstances are obviously exceptional. Word of Khachiyan's result has spread extraordinarily fast, much faster than comprehension of its significance. A variety of issues have in general not been well understood, including the exact character of the ellipsoid method and of Khachiyan's result on polynomiality, its practical significance in linear programming, its implementation, its potential applicability to problems outside of the domain of linear programming, and its relationship to earlier work. Our aim here is to help clarify these important issues in the context of a survey of the ellipsoid method, its historical antecedents, recent developments, and current research
3 editions published in 1980 in English and held by 4 WorldCat member libraries worldwide
IN February 1979 a note by L.G. Khachiyan indicated how an ellipsoid method for linear programming can be implemented in polynomial time. This result has caused great excitement and stimulated a flood of technical papers. Ordinarily there would be no need for a survey of work so recent. The current circumstances are obviously exceptional. Word of Khachiyan's result has spread extraordinarily fast, much faster than comprehension of its significance. A variety of issues have in general not been well understood, including the exact character of the ellipsoid method and of Khachiyan's result on polynomiality, its practical significance in linear programming, its implementation, its potential applicability to problems outside of the domain of linear programming, and its relationship to earlier work. Our aim here is to help clarify these important issues in the context of a survey of the ellipsoid method, its historical antecedents, recent developments, and current research
Structures of some flexible molecules by gas phase electron diffraction by
Michael J Todd(
)
3 editions published in 1982 in English and held by 4 WorldCat member libraries worldwide
3 editions published in 1982 in English and held by 4 WorldCat member libraries worldwide
A Centered Projective Algorithm for Linear Programming by
Michael J Todd(
Book
)
4 editions published between 1987 and 1989 in English and held by 3 WorldCat member libraries worldwide
We describe a projective algorithm for linear programming that shares features with Karmarkar's projective algorithm and its variants and with the pathfollowing methods of Gonzaga, KojimaMizunoYoshise, MonteiroAdler, Renegar, Vaidya and Ye. It operates in a primaldual setting, stays close to the central trajectories, and converges in O the square root of n x L iterations like the latter methods. (Here n is the number of variables and L the input size of the problem.) However, it is motivated by seeking reductions in a suitable potential function as in projective algorithms, and the approximate centering is an automatic byproduct of our choice of potential function
4 editions published between 1987 and 1989 in English and held by 3 WorldCat member libraries worldwide
We describe a projective algorithm for linear programming that shares features with Karmarkar's projective algorithm and its variants and with the pathfollowing methods of Gonzaga, KojimaMizunoYoshise, MonteiroAdler, Renegar, Vaidya and Ye. It operates in a primaldual setting, stays close to the central trajectories, and converges in O the square root of n x L iterations like the latter methods. (Here n is the number of variables and L the input size of the problem.) However, it is motivated by seeking reductions in a suitable potential function as in projective algorithms, and the approximate centering is an automatic byproduct of our choice of potential function
Foundations of computational mathematics, Santander 2005 by
L. M Pardo(
Book
)
4 editions published in 2006 in English and held by 2 WorldCat member libraries worldwide
This volume is a collection of articles based on the plenary talks presented at the 2005 meeting in Santander of the Society for the Foundations of Computational Mathematics. The talks were given by some of the foremost world authorities in computational mathematics. The topics covered reflect the breadth of research within the area as well as the richness and fertility of interactions between seemingly unrelated branches of pure and applied mathematics. As a result this volume will be of interest to researchers in the field of computational mathematics and also to nonexperts who wish to gain some insight into the state of the art in this active and significant field
4 editions published in 2006 in English and held by 2 WorldCat member libraries worldwide
This volume is a collection of articles based on the plenary talks presented at the 2005 meeting in Santander of the Society for the Foundations of Computational Mathematics. The talks were given by some of the foremost world authorities in computational mathematics. The topics covered reflect the breadth of research within the area as well as the richness and fertility of interactions between seemingly unrelated branches of pure and applied mathematics. As a result this volume will be of interest to researchers in the field of computational mathematics and also to nonexperts who wish to gain some insight into the state of the art in this active and significant field
Solving LP problems via weighted centers by Aiping Liao(
Book
)
2 editions published in 1993 in English and held by 2 WorldCat member libraries worldwide
2 editions published in 1993 in English and held by 2 WorldCat member libraries worldwide
Foundations of Computational Mathematics, Hong Kong 2008 by
Felipe Cucker(
)
1 edition published in 2009 in English and held by 0 WorldCat member libraries worldwide
1 edition published in 2009 in English and held by 0 WorldCat member libraries worldwide
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Related Identities
 Nemhauser, George L. Editor
 Rinnooy Kan, A. H. G. 1949 Editor
 Pinkus, Allan 1946 Editor
 Lagarias, Jeffrey C. 1949 Other Author Editor
 Cucker, Felipe 1958 Author Editor
 Pardo, L. M. (Luis M.) Author Editor
 Suli, Endre Editor
 Foster Care Federation (N.Z.)
 Intensive Foster Care Scheme
 Thomson, Jane (Jane Rosalind Masterman) Author
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Associated Subjects
Algorithms Canada Chemistry, Physical and theoretical Children's stories, Afrikaans Competencybased education Computational complexity Computer algorithms Convex programming Cylinders Data compression (Computer science) Economics Economics, Mathematical Ellipse English languageStudy and teaching (Primary) Fixed point theory Foster home care Image processing Linear programming Mathematical optimization Mathematics MathematicsData processing New Zealand Numerical analysis Pattern perception Pattern recognition systems Programming (Mathematics) Reading (Primary) Scientists South Africa Triangulating manifolds United States Word recognitionStudy and teaching (Primary)
Alternative Names
Michael Jeremy Todd britischer Mathematiker
Michael Jeremy Todd British mathematician
Michael Jeremy Todd Brits wiskundige
Michael Jeremy Todd mathématicien britannique
Todd, M. 1947
Todd, M. Dž.
Todd, M. Dž 1947
Todd, M. J.
Todd, M. J. 1947
Todd, M. J. (Michael J.), 1947
Todd, Majkl Dž.
Todd, Michael J.
Todd, Michael Jeremy 1947
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