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Hamiltonian and Gradient Flows, Algorithms and Control
 
Edited by: Anthony Bloch University of Michigan, Ann Arbor, MI
A co-publication of the AMS and Fields Institute
Hamiltonian and Gradient Flows, Algorithms and Control
Hardcover ISBN:  978-0-8218-0255-7
Product Code:  FIC/3
List Price: $103.00
MAA Member Price: $92.70
AMS Member Price: $82.40
eBook ISBN:  978-1-4704-2971-3
Product Code:  FIC/3.E
List Price: $97.00
MAA Member Price: $87.30
AMS Member Price: $77.60
Hardcover ISBN:  978-0-8218-0255-7
eBook: ISBN:  978-1-4704-2971-3
Product Code:  FIC/3.B
List Price: $200.00 $151.50
MAA Member Price: $180.00 $136.35
AMS Member Price: $160.00 $121.20
Hamiltonian and Gradient Flows, Algorithms and Control
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Hamiltonian and Gradient Flows, Algorithms and Control
Edited by: Anthony Bloch University of Michigan, Ann Arbor, MI
A co-publication of the AMS and Fields Institute
Hardcover ISBN:  978-0-8218-0255-7
Product Code:  FIC/3
List Price: $103.00
MAA Member Price: $92.70
AMS Member Price: $82.40
eBook ISBN:  978-1-4704-2971-3
Product Code:  FIC/3.E
List Price: $97.00
MAA Member Price: $87.30
AMS Member Price: $77.60
Hardcover ISBN:  978-0-8218-0255-7
eBook ISBN:  978-1-4704-2971-3
Product Code:  FIC/3.B
List Price: $200.00 $151.50
MAA Member Price: $180.00 $136.35
AMS Member Price: $160.00 $121.20
  • Book Details
     
     
    Fields Institute Communications
    Volume: 31994; 155 pp
    MSC: Primary 34; 70; 93; 65; 90;

    This volume brings together ideas from several areas of mathematics that have traditionally been rather disparate. The conference at The Fields Institute which gave rise to these proceedings was intended to encourage such connections. One of the key interactions occurs between dynamical systems and algorithms, one example being the by now classic observation that the QR algorithm for diagonalizing matrices may be viewed as the time-1 map of the Toda lattice flow. Another link occurs with interior point methods for linear programming, where certain smooth flows associated with such programming problems have proved valuable in the analysis of the corresponding discrete problems. More recently, other smooth flows have been introduced which carry out discrete computations (such as sorting sets of numbers) and which solve certain least squares problems. Another interesting facet of the flows described here is that they often have a dual Hamiltonian and gradient structure, both of which turn out to be useful in analyzing and designing algorithms for solving optimization problems. This volume explores many of these interactions, as well as related work in optimal control and partial differential equations.

    Titles in this series are co-published with the Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada).

    Readership

    Mathematicians and engineers interested in dynamics, optimization, control theory, Hamiltonian and integrable systems, numerical analysis, and linear programming.

  • Table of Contents
     
     
    • Chapters
    • Mark Alber and Jerrold Marsden — Resonant geometric phases for soliton equations
    • Gregory Ammar and William Gragg — Schur flows for orthogonal Hessenberg matrices
    • Anthony Bloch, Peter Crouch and Tudor Ratiu — Sub-Riemannian optimal control problems
    • O. Bogoyavlenskii — Systems of hydrodynamic type, connected with the toda lattice and the Volterra model
    • Roger Brockett — The double bracket equation as the solution of a variational problem
    • Jean-Philippe Brunet — Integration and visualization of matrix orbits on the connection machine
    • Moody Chu — A list of matrix flows with applications
    • Leonid Faybusovich — The Gibbs variational principle, gradient flows, and interior-point methods
    • Steven Smith — Optimization techniques on Riemannian manifolds
    • Bernd Sturmfels — On the number of real roots of a sparse polynomial system
    • Wing Wong — Gradient flows for local minima of combinatorial optimization problems
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Volume: 31994; 155 pp
MSC: Primary 34; 70; 93; 65; 90;

This volume brings together ideas from several areas of mathematics that have traditionally been rather disparate. The conference at The Fields Institute which gave rise to these proceedings was intended to encourage such connections. One of the key interactions occurs between dynamical systems and algorithms, one example being the by now classic observation that the QR algorithm for diagonalizing matrices may be viewed as the time-1 map of the Toda lattice flow. Another link occurs with interior point methods for linear programming, where certain smooth flows associated with such programming problems have proved valuable in the analysis of the corresponding discrete problems. More recently, other smooth flows have been introduced which carry out discrete computations (such as sorting sets of numbers) and which solve certain least squares problems. Another interesting facet of the flows described here is that they often have a dual Hamiltonian and gradient structure, both of which turn out to be useful in analyzing and designing algorithms for solving optimization problems. This volume explores many of these interactions, as well as related work in optimal control and partial differential equations.

Titles in this series are co-published with the Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada).

Readership

Mathematicians and engineers interested in dynamics, optimization, control theory, Hamiltonian and integrable systems, numerical analysis, and linear programming.

  • Chapters
  • Mark Alber and Jerrold Marsden — Resonant geometric phases for soliton equations
  • Gregory Ammar and William Gragg — Schur flows for orthogonal Hessenberg matrices
  • Anthony Bloch, Peter Crouch and Tudor Ratiu — Sub-Riemannian optimal control problems
  • O. Bogoyavlenskii — Systems of hydrodynamic type, connected with the toda lattice and the Volterra model
  • Roger Brockett — The double bracket equation as the solution of a variational problem
  • Jean-Philippe Brunet — Integration and visualization of matrix orbits on the connection machine
  • Moody Chu — A list of matrix flows with applications
  • Leonid Faybusovich — The Gibbs variational principle, gradient flows, and interior-point methods
  • Steven Smith — Optimization techniques on Riemannian manifolds
  • Bernd Sturmfels — On the number of real roots of a sparse polynomial system
  • Wing Wong — Gradient flows for local minima of combinatorial optimization problems
Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.