Variational optimisation by the solution of a series of Hamilton-Jacobi equations

Prasana K. Venkatesh; Linda R. Petzold; Robert W. Carr; Morrel H. Cohen; Anthony M. Dean

doi:10.1016/S0167-2789(01)00222-6

Variational optimisation by the solution of a series of Hamilton-Jacobi equations

Prasana K. Venkatesh, Linda R. Petzold, Robert W. Carr, Morrel H. Cohen, Anthony M. Dean

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

We present a unified scheme which, by combining backward differentiation formulae and variational optimisation theory, significantly extends the scope of both concepts and their application to optimisation problems wherein the constituent dynamics consist of widely disparate scales. Our approach is based on the time-integration of a series of matrix Riccati expressions which satisfy a Hamilton-Jacobi equation.

Original language	English (US)
Pages (from-to)	15-25
Number of pages	11
Journal	Physica D: Nonlinear Phenomena
Volume	154
Issue number	1-2
DOIs	https://doi.org/10.1016/S0167-2789(01)00222-6
State	Published - Jun 1 2001
Externally published	Yes

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics
Condensed Matter Physics
Applied Mathematics

Keywords

Hamilton-Jacobi equation
Optimisation problem
Time-integration
Variational optimisation theory

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10.1016/S0167-2789(01)00222-6

Cite this

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title = "Variational optimisation by the solution of a series of Hamilton-Jacobi equations",

abstract = "We present a unified scheme which, by combining backward differentiation formulae and variational optimisation theory, significantly extends the scope of both concepts and their application to optimisation problems wherein the constituent dynamics consist of widely disparate scales. Our approach is based on the time-integration of a series of matrix Riccati expressions which satisfy a Hamilton-Jacobi equation.",

keywords = "Hamilton-Jacobi equation, Optimisation problem, Time-integration, Variational optimisation theory",

author = "Venkatesh, {Prasana K.} and Petzold, {Linda R.} and Carr, {Robert W.} and Cohen, {Morrel H.} and Dean, {Anthony M.}",

note = "Funding Information: This work has been supported by the National Science Foundation under grant number NSF/CTS-9504827 and also by the Exxon Research and Engineering Company.",

year = "2001",

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doi = "10.1016/S0167-2789(01)00222-6",

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T1 - Variational optimisation by the solution of a series of Hamilton-Jacobi equations

AU - Venkatesh, Prasana K.

AU - Petzold, Linda R.

AU - Carr, Robert W.

AU - Cohen, Morrel H.

AU - Dean, Anthony M.

N1 - Funding Information: This work has been supported by the National Science Foundation under grant number NSF/CTS-9504827 and also by the Exxon Research and Engineering Company.

PY - 2001/6/1

Y1 - 2001/6/1

N2 - We present a unified scheme which, by combining backward differentiation formulae and variational optimisation theory, significantly extends the scope of both concepts and their application to optimisation problems wherein the constituent dynamics consist of widely disparate scales. Our approach is based on the time-integration of a series of matrix Riccati expressions which satisfy a Hamilton-Jacobi equation.

AB - We present a unified scheme which, by combining backward differentiation formulae and variational optimisation theory, significantly extends the scope of both concepts and their application to optimisation problems wherein the constituent dynamics consist of widely disparate scales. Our approach is based on the time-integration of a series of matrix Riccati expressions which satisfy a Hamilton-Jacobi equation.

KW - Hamilton-Jacobi equation

KW - Optimisation problem

KW - Time-integration

KW - Variational optimisation theory

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VL - 154

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EP - 25

JO - Physica D: Nonlinear Phenomena

JF - Physica D: Nonlinear Phenomena

IS - 1-2

ER -

Variational optimisation by the solution of a series of Hamilton-Jacobi equations

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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