Category:AMPL - Revision history

SebastianSager: Removed problem characterization category

2016-01-28T08:56:51Z

Removed problem characterization category

← Older revision		Revision as of 08:56, 28 January 2016
Line 1:		Line 1:
	This category lists all problems for which [http://www.ampl.org AMPL] code is provided. AMPL ~~does not support differential equations~~, ~~hence all models are~~ a (~~finite~~-~~dimensional~~) ~~discretization in one sense or another of~~ a ~~control problem~~.		This category lists all problems for which [http://www.ampl.org AMPL] code is provided. AMPL is a modeling language for mathematical programming, comparable to GAMS and ZIMBL. Its modeling syntax is very close to the mathematical one, and a wide range of linear and nonlinear (mixed-integer) solvers are interfaced. It comes with a commercial licence (free student version limited by 300 variables).

	~~MIOCPs include features related to different mathematical disciplines. Hence, it is~~ not ~~surprising that very different approaches have been proposed to analyze and solve them. There are three generic approaches to solve model-based optimal~~ control problems, ~~compare <bib id="Binder2001" />: first, solution of the Hamilton-Jacobi-Bellman equation and in~~ a ~~discrete setting Dynamic Programming, second indirect methods, also known as the first optimize, then discretize approach, and third direct methods~~ (~~first optimize, then discretize~~) ~~and~~ in particular all--at--once approaches that solve the simulation and the optimization task simultaneously. The combination with the additional combinatorial restrictions on control functions comes at different levels: for free in dynamic programming, as the control ~~space is evaluated anyhow, by means of an enumeration in the inner optimization~~ problem ~~of the necessary conditions of optimality in Pontryagin's maximum principle, or by various methods from integer programming in the direct methods~~.		AMPL does not directly support control problems or differential equations, hence all models are a (finite-dimensional) discretization in one sense or another of a control problem.

	~~Even in the case of direct methods~~, ~~there are multiple alternatives to proceed. Various approaches have been proposed to discretize the differential equations~~ by means of ~~shooting methods or collocation, e~~.~~g., <bib id="Bock1984" />,<bib id="Biegler1984" />, to (re)formulate~~ the ~~control problem by outer convexification <bib id="Sager2009" />,~~ to ~~use global optimization methods by under- and overestimators~~, e.g., ~~<bib id="Esposito2000" />,<bib id="Papamichail2004" />,<bib id="Chachuat2006" />, to optimize the time-points for~~ a given switching structure, e.g., <bib id="Kaya2003" />,<bib id="Gerdts2006" />,<bib id="Sager2009" />, to consider a static optimization problem instead of the transient behavior, e.g., <bib id="Grossmann2005" />, to approximate nonlinearities by piecewise-linear functions, e.g., <bib id="Martin2006" />, or by approximating the combinatorial decisions by continuous formulations, as in <bib id="Burgschweiger2009" /> for drinking water networks.		They can be either obtained by hand, or by means of an automatized export. One example are the compilers available to process [[:Category:optimica \| optimica]] models that automatically generate AMPL output, e.g., by applying a Radau collocation.

	We do not want to discuss these methods here, but rather refer to <bib id="Sager2009" />,<bib id="Sager2009b" /> for more comprehensive surveys. The main purpose of mentioning them is to point out that they all discretize the optimization problem in function space in a different manner, and hence result in different mathematical problems that are actually solved on a computer.		Recently, the [[:Category:AMPL/TACO \| TACO Toolkit for AMPL Control Optimization]] is a new effort aimed at modeling optimal control problems in AMPL. A small set of extensions allows to decouple the choice of a discretization scheme from the actual AMPL model. [[:Category:Muscod \| MUSCOD-II]] is the first solver to support AMPL models using the TACO extension.

	Powerful commercial MILP solvers and advances in MINLP solvers make the usage of general purpose MILP/MINLP solvers more and more attractive. ''Please be aware however that the MINLP formulations we provide in this category are only one out of many possible ways to formulate the underlying MIOCP problems.''

	~~There are compilers available to process [[:Category:optimica \| optimica]] models and automatically generate AMPL output, e.g., by applying a Radau collocation.~~

	Recently, the [[:Category:AMPL/TACO \| TACO Toolkit for AMPL Control Optimization]] is a new effort aimed at modeling optimal control problems in AMPL. A small set of extensions allows to decouple the choice of a discretization scheme from the actual AMPL model. MUSCOD-II ~~(Heidelberg) will be~~ the first solver to support AMPL models using the TACO ~~extensions~~.

	== References ==		== References ==
	<biblist />		<biblist />

			[[Category: Implementation]]
	~~<!--List of all categories this page is part of. List characterization of solution behavior, model properties, ore presence of implementation details (e.g., AMPL for AMPL model) here -->~~
	~~[[Category:Problem characterization]]~~ [[Category: Implementation]]

FelixMueller at 18:19, 27 January 2016

2016-01-27T18:19:15Z

← Older revision		Revision as of 18:19, 27 January 2016
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	<!--List of all categories this page is part of. List characterization of solution behavior, model properties, ore presence of implementation details (e.g., AMPL for AMPL model) here -->		<!--List of all categories this page is part of. List characterization of solution behavior, model properties, ore presence of implementation details (e.g., AMPL for AMPL model) here -->
	[[Category:Problem characterization]]		[[Category:Problem characterization]] [[Category: Implementation]]

JonasSchulze: Text replacement - "" to ""

2016-01-23T10:10:59Z

Text replacement - "<bibreferences/>" to "<biblist />"

← Older revision		Revision as of 10:10, 23 January 2016
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	== References ==		== References ==
	<~~bibreferences~~/>		<biblist />


	<!--List of all categories this page is part of. List characterization of solution behavior, model properties, ore presence of implementation details (e.g., AMPL for AMPL model) here -->		<!--List of all categories this page is part of. List characterization of solution behavior, model properties, ore presence of implementation details (e.g., AMPL for AMPL model) here -->
	[[Category:Problem characterization]]		[[Category:Problem characterization]]

JonasSchulze: Text replacement - "\(.*)\<\/bibref\>" to ""

2016-01-20T17:54:24Z

Text replacement - "\<bibref\>(.*)\<\/bibref\>" to "<bib id="$1" />"

← Older revision		Revision as of 17:54, 20 January 2016
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	This category lists all problems for which [http://www.ampl.org AMPL] code is provided. AMPL does not support differential equations, hence all models are a (finite-dimensional) discretization in one sense or another of a control problem.		This category lists all problems for which [http://www.ampl.org AMPL] code is provided. AMPL does not support differential equations, hence all models are a (finite-dimensional) discretization in one sense or another of a control problem.

	MIOCPs include features related to different mathematical disciplines. Hence, it is not surprising that very different approaches have been proposed to analyze and solve them. There are three generic approaches to solve model-based optimal control problems, compare <~~bibref>~~Binder2001</~~bibref~~>: first, solution of the Hamilton-Jacobi-Bellman equation and in a discrete setting Dynamic Programming, second indirect methods, also known as the first optimize, then discretize approach, and third direct methods (first optimize, then discretize) and in particular all--at--once approaches that solve the simulation and the optimization task simultaneously. The combination with the additional combinatorial restrictions on control functions comes at different levels: for free in dynamic programming, as the control space is evaluated anyhow, by means of an enumeration in the inner optimization problem of the necessary conditions of optimality in Pontryagin's maximum principle, or by various methods from integer programming in the direct methods.		MIOCPs include features related to different mathematical disciplines. Hence, it is not surprising that very different approaches have been proposed to analyze and solve them. There are three generic approaches to solve model-based optimal control problems, compare <bib id="Binder2001" />: first, solution of the Hamilton-Jacobi-Bellman equation and in a discrete setting Dynamic Programming, second indirect methods, also known as the first optimize, then discretize approach, and third direct methods (first optimize, then discretize) and in particular all--at--once approaches that solve the simulation and the optimization task simultaneously. The combination with the additional combinatorial restrictions on control functions comes at different levels: for free in dynamic programming, as the control space is evaluated anyhow, by means of an enumeration in the inner optimization problem of the necessary conditions of optimality in Pontryagin's maximum principle, or by various methods from integer programming in the direct methods.

	Even in the case of direct methods, there are multiple alternatives to proceed. Various approaches have been proposed to discretize the differential equations by means of shooting methods or collocation, e.g., <~~bibref>~~Bock1984</~~bibref~~>,<~~bibref>~~Biegler1984</~~bibref~~>, to (re)formulate the control problem by outer convexification <~~bibref>~~Sager2009</~~bibref~~>, to use global optimization methods by under- and overestimators, e.g., <~~bibref>~~Esposito2000</~~bibref~~>,<~~bibref>~~Papamichail2004</~~bibref~~>,<~~bibref>~~Chachuat2006</~~bibref~~>, to optimize the time-points for a given switching structure, e.g., <~~bibref>~~Kaya2003</~~bibref~~>,<~~bibref>~~Gerdts2006</~~bibref~~>,<~~bibref>~~Sager2009</~~bibref~~>, to consider a static optimization problem instead of the transient behavior, e.g., <~~bibref>~~Grossmann2005</~~bibref~~>, to approximate nonlinearities by piecewise-linear functions, e.g., <~~bibref>~~Martin2006</~~bibref~~>, or by approximating the combinatorial decisions by continuous formulations, as in <~~bibref>~~Burgschweiger2009</~~bibref~~> for drinking water networks.		Even in the case of direct methods, there are multiple alternatives to proceed. Various approaches have been proposed to discretize the differential equations by means of shooting methods or collocation, e.g., <bib id="Bock1984" />,<bib id="Biegler1984" />, to (re)formulate the control problem by outer convexification <bib id="Sager2009" />, to use global optimization methods by under- and overestimators, e.g., <bib id="Esposito2000" />,<bib id="Papamichail2004" />,<bib id="Chachuat2006" />, to optimize the time-points for a given switching structure, e.g., <bib id="Kaya2003" />,<bib id="Gerdts2006" />,<bib id="Sager2009" />, to consider a static optimization problem instead of the transient behavior, e.g., <bib id="Grossmann2005" />, to approximate nonlinearities by piecewise-linear functions, e.g., <bib id="Martin2006" />, or by approximating the combinatorial decisions by continuous formulations, as in <bib id="Burgschweiger2009" /> for drinking water networks.

	We do not want to discuss these methods here, but rather refer to <~~bibref>~~Sager2009</~~bibref~~>,<~~bibref>~~Sager2009b</~~bibref~~> for more comprehensive surveys. The main purpose of mentioning them is to point out that they all discretize the optimization problem in function space in a different manner, and hence result in different mathematical problems that are actually solved on a computer.		We do not want to discuss these methods here, but rather refer to <bib id="Sager2009" />,<bib id="Sager2009b" /> for more comprehensive surveys. The main purpose of mentioning them is to point out that they all discretize the optimization problem in function space in a different manner, and hence result in different mathematical problems that are actually solved on a computer.

	Powerful commercial MILP solvers and advances in MINLP solvers make the usage of general purpose MILP/MINLP solvers more and more attractive. ''Please be aware however that the MINLP formulations we provide in this category are only one out of many possible ways to formulate the underlying MIOCP problems.''		Powerful commercial MILP solvers and advances in MINLP solvers make the usage of general purpose MILP/MINLP solvers more and more attractive. ''Please be aware however that the MINLP formulations we provide in this category are only one out of many possible ways to formulate the underlying MIOCP problems.''

FelixMueller at 10:35, 15 December 2015

2015-12-15T10:35:32Z

← Older revision		Revision as of 10:35, 15 December 2015
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	<bibreferences/>		<bibreferences/>


			<!--List of all categories this page is part of. List characterization of solution behavior, model properties, ore presence of implementation details (e.g., AMPL for AMPL model) here -->
	[[Category:Problem characterization]]		[[Category:Problem characterization]]

Ckirches at 17:34, 29 September 2011

2011-09-29T17:34:59Z

← Older revision		Revision as of 17:34, 29 September 2011
Line 11:		Line 11:
	There are compilers available to process [[:Category:optimica \| optimica]] models and automatically generate AMPL output, e.g., by applying a Radau collocation.		There are compilers available to process [[:Category:optimica \| optimica]] models and automatically generate AMPL output, e.g., by applying a Radau collocation.

	Recently, the [[Category:AMPL/TACO \| TACO Toolkit for AMPL Control Optimization]] is a new effort aimed at modeling optimal control problems in AMPL. A small set of extensions allows to decouple the choice of a discretization scheme from the actual AMPL model. MUSCOD-II (Heidelberg) will be the first solver to support AMPL models using the TACO extensions.		Recently, the [[:Category:AMPL/TACO \| TACO Toolkit for AMPL Control Optimization]] is a new effort aimed at modeling optimal control problems in AMPL. A small set of extensions allows to decouple the choice of a discretization scheme from the actual AMPL model. MUSCOD-II (Heidelberg) will be the first solver to support AMPL models using the TACO extensions.

	== References ==		== References ==

Ckirches: Mention TACO

2011-09-29T17:31:44Z

Mention TACO

← Older revision		Revision as of 17:31, 29 September 2011
Line 9:		Line 9:
	Powerful commercial MILP solvers and advances in MINLP solvers make the usage of general purpose MILP/MINLP solvers more and more attractive. ''Please be aware however that the MINLP formulations we provide in this category are only one out of many possible ways to formulate the underlying MIOCP problems.''		Powerful commercial MILP solvers and advances in MINLP solvers make the usage of general purpose MILP/MINLP solvers more and more attractive. ''Please be aware however that the MINLP formulations we provide in this category are only one out of many possible ways to formulate the underlying MIOCP problems.''

	~~Hint: there~~ are compilers available to process [[:Category:optimica \| optimica]] models and automatically generate AMPL output, e.g., by applying a Radau collocation.		There are compilers available to process [[:Category:optimica \| optimica]] models and automatically generate AMPL output, e.g., by applying a Radau collocation.

			Recently, the [[Category:AMPL/TACO \| TACO Toolkit for AMPL Control Optimization]] is a new effort aimed at modeling optimal control problems in AMPL. A small set of extensions allows to decouple the choice of a discretization scheme from the actual AMPL model. MUSCOD-II (Heidelberg) will be the first solver to support AMPL models using the TACO extensions.

	== References ==		== References ==

SebastianSager at 16:20, 11 August 2009

2009-08-11T16:20:56Z

← Older revision		Revision as of 16:20, 11 August 2009
Line 8:		Line 8:

	Powerful commercial MILP solvers and advances in MINLP solvers make the usage of general purpose MILP/MINLP solvers more and more attractive. ''Please be aware however that the MINLP formulations we provide in this category are only one out of many possible ways to formulate the underlying MIOCP problems.''		Powerful commercial MILP solvers and advances in MINLP solvers make the usage of general purpose MILP/MINLP solvers more and more attractive. ''Please be aware however that the MINLP formulations we provide in this category are only one out of many possible ways to formulate the underlying MIOCP problems.''

			Hint: there are compilers available to process [[:Category:optimica \| optimica]] models and automatically generate AMPL output, e.g., by applying a Radau collocation.

	== References ==		== References ==

SebastianSager: Fixed bibliography and text

2009-07-09T15:29:59Z

Fixed bibliography and text

← Older revision		Revision as of 15:29, 9 July 2009
Line 3:		Line 3:
	MIOCPs include features related to different mathematical disciplines. Hence, it is not surprising that very different approaches have been proposed to analyze and solve them. There are three generic approaches to solve model-based optimal control problems, compare <bibref>Binder2001</bibref>: first, solution of the Hamilton-Jacobi-Bellman equation and in a discrete setting Dynamic Programming, second indirect methods, also known as the first optimize, then discretize approach, and third direct methods (first optimize, then discretize) and in particular all--at--once approaches that solve the simulation and the optimization task simultaneously. The combination with the additional combinatorial restrictions on control functions comes at different levels: for free in dynamic programming, as the control space is evaluated anyhow, by means of an enumeration in the inner optimization problem of the necessary conditions of optimality in Pontryagin's maximum principle, or by various methods from integer programming in the direct methods.		MIOCPs include features related to different mathematical disciplines. Hence, it is not surprising that very different approaches have been proposed to analyze and solve them. There are three generic approaches to solve model-based optimal control problems, compare <bibref>Binder2001</bibref>: first, solution of the Hamilton-Jacobi-Bellman equation and in a discrete setting Dynamic Programming, second indirect methods, also known as the first optimize, then discretize approach, and third direct methods (first optimize, then discretize) and in particular all--at--once approaches that solve the simulation and the optimization task simultaneously. The combination with the additional combinatorial restrictions on control functions comes at different levels: for free in dynamic programming, as the control space is evaluated anyhow, by means of an enumeration in the inner optimization problem of the necessary conditions of optimality in Pontryagin's maximum principle, or by various methods from integer programming in the direct methods.

	Even in the case of direct methods, there are multiple alternatives to proceed. Various approaches have been proposed to discretize the differential equations by means of shooting methods or collocation, e.g., <bibref>Bock1984,Biegler1984</bibref>, to (re)formulate the control problem by outer convexification <bibref>Sager2009</bibref>, to use global optimization methods by under- and overestimators, e.g., <bibref>Esposito2000,Papamichail2004,Chachuat2006</bibref>, to optimize the time-points for a given switching structure, e.g., <bibref>Kaya2003,Gerdts2006,Sager2009</bibref>, to consider a static optimization problem instead of the transient behavior, e.g., <bibref>Grossmann2005</bibref>, to approximate nonlinearities by piecewise-linear functions, e.g., <bibref>Martin2006</bibref>, or by approximating the combinatorial decisions by continuous formulations, as in <bibref>Burgschweiger2009</bibref> for drinking water networks.		Even in the case of direct methods, there are multiple alternatives to proceed. Various approaches have been proposed to discretize the differential equations by means of shooting methods or collocation, e.g., <bibref>Bock1984</bibref>,<bibref>Biegler1984</bibref>, to (re)formulate the control problem by outer convexification <bibref>Sager2009</bibref>, to use global optimization methods by under- and overestimators, e.g., <bibref>Esposito2000</bibref>,<bibref>Papamichail2004</bibref>,<bibref>Chachuat2006</bibref>, to optimize the time-points for a given switching structure, e.g., <bibref>Kaya2003</bibref>,<bibref>Gerdts2006</bibref>,<bibref>Sager2009</bibref>, to consider a static optimization problem instead of the transient behavior, e.g., <bibref>Grossmann2005</bibref>, to approximate nonlinearities by piecewise-linear functions, e.g., <bibref>Martin2006</bibref>, or by approximating the combinatorial decisions by continuous formulations, as in <bibref>Burgschweiger2009</bibref> for drinking water networks.

	We do not want to discuss these methods here, but rather refer to <bibref>Sager2009,Sager2009b</bibref> for more comprehensive surveys. The main purpose of mentioning them is to point out that they all discretize the optimization problem in function space in a different manner, and hence result in different mathematical problems that are actually solved on a computer.		We do not want to discuss these methods here, but rather refer to <bibref>Sager2009</bibref>,<bibref>Sager2009b</bibref> for more comprehensive surveys. The main purpose of mentioning them is to point out that they all discretize the optimization problem in function space in a different manner, and hence result in different mathematical problems that are actually solved on a computer.

	Powerful commercial MILP solvers and advances in MINLP solvers ~~as described in the other contributions to this book~~ make the usage of general purpose MILP/MINLP solvers more and more attractive. Please be aware however that the MINLP formulations we provide in this category are only one out of many possible ways to formulate the underlying MIOCP problems.		Powerful commercial MILP solvers and advances in MINLP solvers make the usage of general purpose MILP/MINLP solvers more and more attractive. ''Please be aware however that the MINLP formulations we provide in this category are only one out of many possible ways to formulate the underlying MIOCP problems.''

			== References ==
			<bibreferences/>

	[[Category:Problem characterization]]		[[Category:Problem characterization]]

SebastianSager: Added introduction part

2009-07-09T13:11:13Z

Added introduction part

← Older revision		Revision as of 13:11, 9 July 2009
Line 1:		Line 1:
	This category lists all problems for which AMPL code is provided.		This category lists all problems for which [http://www.ampl.org AMPL] code is provided. AMPL does not support differential equations, hence all models are a (finite-dimensional) discretization in one sense or another of a control problem.

			MIOCPs include features related to different mathematical disciplines. Hence, it is not surprising that very different approaches have been proposed to analyze and solve them. There are three generic approaches to solve model-based optimal control problems, compare <bibref>Binder2001</bibref>: first, solution of the Hamilton-Jacobi-Bellman equation and in a discrete setting Dynamic Programming, second indirect methods, also known as the first optimize, then discretize approach, and third direct methods (first optimize, then discretize) and in particular all--at--once approaches that solve the simulation and the optimization task simultaneously. The combination with the additional combinatorial restrictions on control functions comes at different levels: for free in dynamic programming, as the control space is evaluated anyhow, by means of an enumeration in the inner optimization problem of the necessary conditions of optimality in Pontryagin's maximum principle, or by various methods from integer programming in the direct methods.

			Even in the case of direct methods, there are multiple alternatives to proceed. Various approaches have been proposed to discretize the differential equations by means of shooting methods or collocation, e.g., <bibref>Bock1984,Biegler1984</bibref>, to (re)formulate the control problem by outer convexification <bibref>Sager2009</bibref>, to use global optimization methods by under- and overestimators, e.g., <bibref>Esposito2000,Papamichail2004,Chachuat2006</bibref>, to optimize the time-points for a given switching structure, e.g., <bibref>Kaya2003,Gerdts2006,Sager2009</bibref>, to consider a static optimization problem instead of the transient behavior, e.g., <bibref>Grossmann2005</bibref>, to approximate nonlinearities by piecewise-linear functions, e.g., <bibref>Martin2006</bibref>, or by approximating the combinatorial decisions by continuous formulations, as in <bibref>Burgschweiger2009</bibref> for drinking water networks.

			We do not want to discuss these methods here, but rather refer to <bibref>Sager2009,Sager2009b</bibref> for more comprehensive surveys. The main purpose of mentioning them is to point out that they all discretize the optimization problem in function space in a different manner, and hence result in different mathematical problems that are actually solved on a computer.

			Powerful commercial MILP solvers and advances in MINLP solvers as described in the other contributions to this book make the usage of general purpose MILP/MINLP solvers more and more attractive. Please be aware however that the MINLP formulations we provide in this category are only one out of many possible ways to formulate the underlying MIOCP problems.


	[[Category:Problem characterization]]		[[Category:Problem characterization]]