Chance constrained programming - Revision history

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2025-06-10T13:25:36Z

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	== Solution Approaches ==		== Solution Approaches ==
	To solve CCP problems, the stochastic optimization problem is often relaxed into an equivalent deterministic problem. There are different approaches depending on the nature of the problem:		To solve CCP problems, the [[stochastic optimization]] problem is often relaxed into an equivalent deterministic problem. There are different approaches depending on the nature of the problem:
	* '''Linear CCP''': For linear systems, the feasible region is typically convex, and the problem can be solved using [[linear programming]] techniques.		* '''Linear CCP''': For linear systems, the feasible region is typically convex, and the problem can be solved using [[linear programming]] techniques.
	* '''Nonlinear CCP''': For nonlinear systems, the main challenge lies in computing the probabilities and their gradients. These problems often require [[nonlinear programming]] solvers.		* '''Nonlinear CCP''': For nonlinear systems, the main challenge lies in computing the probabilities and their gradients. These problems often require [[nonlinear programming]] solvers.
	* '''Dynamic Systems''': Dynamic systems involve time-dependent uncertainties, and the solution approach must account for the propagation of uncertainty over time.<ref name=pu/>		* '''Dynamic Systems''': Dynamic systems involve time-dependent uncertainties, and the solution approach must account for the [[propagation of uncertainty]] over time.<ref name=pu/>

	== Practical Applications ==		== Practical Applications ==

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2024-12-15T06:24:23Z

Alter: pages, issue. Added issue. Formatted dashes. | Use this bot. Report bugs. | Suggested by Dominic3203 | Category:Stochastic optimization | #UCB_Category 13/27

← Previous revision		Revision as of 06:24, 15 December 2024
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	'''Chance Constrained Programming (CCP)''' is a [[mathematical optimization]] approach used to handle problems under uncertainty. It was first introduced by [[Abraham Charnes\|Charnes]] and [[William W. Cooper\|Cooper]] in 1959 and further developed by Miller and Wagner in 1965.<ref>{{cite journal \|last1=Charnes \|first1=Abraham \|last2=Cooper \|first2=William W. \|title=Chance-Constrained Programming \|journal=Management Science \|date=1959 \|volume=6 \|issue=1 \|pages=~~73-79~~ \|doi=10.1287/mnsc.6.1.73}}</ref><ref>{{cite journal \|last1=Miller \|first1=L. R. \|last2=Wagner \|first2=H. M. \|title=Chance-constrained programming with joint constraints \|journal=Operations Research \|date=1965 \|volume=13 \|issue=6 \|pages=~~930-945~~ \|doi=10.1287/opre.13.6.930}}</ref> CCP is widely used in various fields, including [[finance]], [[engineering]], and [[operations research]], to optimize decision-making processes where certain constraints need to be satisfied with a specified probability.		'''Chance Constrained Programming (CCP)''' is a [[mathematical optimization]] approach used to handle problems under uncertainty. It was first introduced by [[Abraham Charnes\|Charnes]] and [[William W. Cooper\|Cooper]] in 1959 and further developed by Miller and Wagner in 1965.<ref>{{cite journal \|last1=Charnes \|first1=Abraham \|last2=Cooper \|first2=William W. \|title=Chance-Constrained Programming \|journal=Management Science \|date=1959 \|volume=6 \|issue=1 \|pages=73–79 \|doi=10.1287/mnsc.6.1.73}}</ref><ref>{{cite journal \|last1=Miller \|first1=L. R. \|last2=Wagner \|first2=H. M. \|title=Chance-constrained programming with joint constraints \|journal=Operations Research \|date=1965 \|volume=13 \|issue=6 \|pages=930–945 \|doi=10.1287/opre.13.6.930}}</ref> CCP is widely used in various fields, including [[finance]], [[engineering]], and [[operations research]], to optimize decision-making processes where certain constraints need to be satisfied with a specified probability.

	== Theoretical Background ==		== Theoretical Background ==
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	== Practical Applications ==		== Practical Applications ==

	Chance constrained programming is used in engineering for process optimisation under uncertainty and production planning and in finance for portfolio selection.<ref name=pu/> It has been applied to [[renewable energy]] integration,<ref>{{cite book \|last1=Zhang \|first1=Ning \|last2=Kang \|first2=Chongqing \|last3=Du \|first3=Ershun \|last4=Wang \|first4=Yi \|title=Analytics and Optimization for Renewable Energy Integration \|date=2019 \|publisher=CRC Press \|isbn=9780429847707 \|page=180}}</ref> generating flight trajectory for [[UAV]]s,<ref>{{cite book \|last1=Chai \|first1=Runqi \|title=Advanced Trajectory Optimization, Guidance and Control Strategies for Aerospace Vehicles \|date=2023 \|publisher=Springer Nature Singapore \|isbn=9789819943111 \|page=131}}</ref> and robotic space exploration.<ref>{{cite journal \|last1=Ono \|first1=Masahiro \|last2=Pavone \|first2=Marco \|last3=Kuwata \|first3=Yoshiaki \|last4=Balaram \|first4=J. \|title=Chance-constrained dynamic programming with application to risk-aware robotic space exploration \|journal=Autonomous Robots \|date=2015 \|volume=39 \|pages=~~555-571~~ \|doi=10.1007/s10514-015-9467-7}}</ref>		Chance constrained programming is used in engineering for process optimisation under uncertainty and production planning and in finance for portfolio selection.<ref name=pu/> It has been applied to [[renewable energy]] integration,<ref>{{cite book \|last1=Zhang \|first1=Ning \|last2=Kang \|first2=Chongqing \|last3=Du \|first3=Ershun \|last4=Wang \|first4=Yi \|title=Analytics and Optimization for Renewable Energy Integration \|date=2019 \|publisher=CRC Press \|isbn=9780429847707 \|page=180}}</ref> generating flight trajectory for [[UAV]]s,<ref>{{cite book \|last1=Chai \|first1=Runqi \|title=Advanced Trajectory Optimization, Guidance and Control Strategies for Aerospace Vehicles \|date=2023 \|publisher=Springer Nature Singapore \|isbn=9789819943111 \|page=131}}</ref> and robotic space exploration.<ref>{{cite journal \|last1=Ono \|first1=Masahiro \|last2=Pavone \|first2=Marco \|last3=Kuwata \|first3=Yoshiaki \|last4=Balaram \|first4=J. \|title=Chance-constrained dynamic programming with application to risk-aware robotic space exploration \|journal=Autonomous Robots \|date=2015 \|volume=39 \|issue=4 \|pages=555–571 \|doi=10.1007/s10514-015-9467-7}}</ref>

	=== Process Optimization Under Uncertainty ===		=== Process Optimization Under Uncertainty ===
	CCP is used in [[chemical engineering\|chemical]] and [[process engineering]] to optimize operations considering uncertainties in operating conditions and model parameters. For example, in optimizing the design and operation of chemical plants, CCP helps in achieving desired performance levels while accounting for uncertainties in feedstock quality, demand, and environmental conditions.<ref name=pu>{{cite journal \|last1=Pu \|first1=Pu \|last2=Arellano-Garcia \|first2=Harvey \|last3=Wozny \|first3=Günter \|title=Chance constrained programming approach to process optimization under uncertainty \|journal=Computers and Chemical Engineering \|date=2008 \|volume=32 \|issue=~~1-2~~ \|pages=~~25-45~~ \|doi=10.1016/j.compchemeng.2007.05.009}}</ref>		CCP is used in [[chemical engineering\|chemical]] and [[process engineering]] to optimize operations considering uncertainties in operating conditions and model parameters. For example, in optimizing the design and operation of chemical plants, CCP helps in achieving desired performance levels while accounting for uncertainties in feedstock quality, demand, and environmental conditions.<ref name=pu>{{cite journal \|last1=Pu \|first1=Pu \|last2=Arellano-Garcia \|first2=Harvey \|last3=Wozny \|first3=Günter \|title=Chance constrained programming approach to process optimization under uncertainty \|journal=Computers and Chemical Engineering \|date=2008 \|volume=32 \|issue=1–2 \|pages=25–45 \|doi=10.1016/j.compchemeng.2007.05.009}}</ref>

	=== Production Planning and Operations ===		=== Production Planning and Operations ===

Aadirulez8: v2.05 - Fix errors for CW project (Link equal to linktext)

2024-10-14T22:09:36Z

v2.05 - Fix errors for CW project (Link equal to linktext)

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	To solve CCP problems, the stochastic optimization problem is often relaxed into an equivalent deterministic problem. There are different approaches depending on the nature of the problem:		To solve CCP problems, the stochastic optimization problem is often relaxed into an equivalent deterministic problem. There are different approaches depending on the nature of the problem:
	* '''Linear CCP''': For linear systems, the feasible region is typically convex, and the problem can be solved using [[linear programming]] techniques.		* '''Linear CCP''': For linear systems, the feasible region is typically convex, and the problem can be solved using [[linear programming]] techniques.
	* '''Nonlinear CCP''': For nonlinear systems, the main challenge lies in computing the probabilities and their gradients. These problems often require [[~~Nonlinear programming\|~~nonlinear programming]] solvers.		* '''Nonlinear CCP''': For nonlinear systems, the main challenge lies in computing the probabilities and their gradients. These problems often require [[nonlinear programming]] solvers.
	* '''Dynamic Systems''': Dynamic systems involve time-dependent uncertainties, and the solution approach must account for the propagation of uncertainty over time.<ref name=pu/>		* '''Dynamic Systems''': Dynamic systems involve time-dependent uncertainties, and the solution approach must account for the propagation of uncertainty over time.<ref name=pu/>

Arjayay: Duplicate word removed

2024-08-09T21:55:01Z

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← Previous revision		Revision as of 21:55, 9 August 2024
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	== Practical Applications ==		== Practical Applications ==

	Chance constrained programming is used in engineering for process optimisation under uncertainty and production planning and in finance ~~for~~ for portfolio selection.<ref name=pu/> It has been applied to [[renewable energy]] integration,<ref>{{cite book \|last1=Zhang \|first1=Ning \|last2=Kang \|first2=Chongqing \|last3=Du \|first3=Ershun \|last4=Wang \|first4=Yi \|title=Analytics and Optimization for Renewable Energy Integration \|date=2019 \|publisher=CRC Press \|isbn=9780429847707 \|page=180}}</ref> generating flight trajectory for [[UAV]]s,<ref>{{cite book \|last1=Chai \|first1=Runqi \|title=Advanced Trajectory Optimization, Guidance and Control Strategies for Aerospace Vehicles \|date=2023 \|publisher=Springer Nature Singapore \|isbn=9789819943111 \|page=131}}</ref> and robotic space exploration.<ref>{{cite journal \|last1=Ono \|first1=Masahiro \|last2=Pavone \|first2=Marco \|last3=Kuwata \|first3=Yoshiaki \|last4=Balaram \|first4=J. \|title=Chance-constrained dynamic programming with application to risk-aware robotic space exploration \|journal=Autonomous Robots \|date=2015 \|volume=39 \|pages=555-571 \|doi=10.1007/s10514-015-9467-7}}</ref>		Chance constrained programming is used in engineering for process optimisation under uncertainty and production planning and in finance for portfolio selection.<ref name=pu/> It has been applied to [[renewable energy]] integration,<ref>{{cite book \|last1=Zhang \|first1=Ning \|last2=Kang \|first2=Chongqing \|last3=Du \|first3=Ershun \|last4=Wang \|first4=Yi \|title=Analytics and Optimization for Renewable Energy Integration \|date=2019 \|publisher=CRC Press \|isbn=9780429847707 \|page=180}}</ref> generating flight trajectory for [[UAV]]s,<ref>{{cite book \|last1=Chai \|first1=Runqi \|title=Advanced Trajectory Optimization, Guidance and Control Strategies for Aerospace Vehicles \|date=2023 \|publisher=Springer Nature Singapore \|isbn=9789819943111 \|page=131}}</ref> and robotic space exploration.<ref>{{cite journal \|last1=Ono \|first1=Masahiro \|last2=Pavone \|first2=Marco \|last3=Kuwata \|first3=Yoshiaki \|last4=Balaram \|first4=J. \|title=Chance-constrained dynamic programming with application to risk-aware robotic space exploration \|journal=Autonomous Robots \|date=2015 \|volume=39 \|pages=555-571 \|doi=10.1007/s10514-015-9467-7}}</ref>

	=== Process Optimization Under Uncertainty ===		=== Process Optimization Under Uncertainty ===

Alaexis at 17:54, 9 August 2024

2024-08-09T17:54:00Z

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	{{Reflist}}		{{Reflist}}

			[[Category:Stochastic optimization]]
	{{Uncategorized\|date=August 2024}}

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	== References ==		== References ==
	{{Reflist}}		{{Reflist}}

			{{Uncategorized\|date=August 2024}}

Alaexis: Alaexis moved page User:Alaexis/optimization to Chance constrained programming: Move to mainspace

2024-08-09T13:52:44Z

Alaexis moved page User:Alaexis/optimization to Chance constrained programming: Move to mainspace

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Alaexis at 13:43, 9 August 2024

2024-08-09T13:43:19Z

← Previous revision		Revision as of 13:43, 9 August 2024
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	'''Chance Constrained Programming (CCP)''' is a [[mathematical optimization]] ~~technique~~ used to handle problems under uncertainty. It was first introduced by [[Abraham Charnes\|Charnes]] and [[William W. Cooper\|Cooper]] in 1959 and further developed by Miller and Wagner in 1965.<ref>{{cite journal \|last1=Charnes \|first1=Abraham \|last2=Cooper \|first2=William W. \|title=Chance-Constrained Programming \|journal=Management Science \|date=1959 \|volume=6 \|issue=1 \|pages=73-79 \|doi=10.1287/mnsc.6.1.73}}</ref><ref>{{cite journal \|last1=Miller \|first1=L. R. \|last2=Wagner \|first2=H. M. \|title=Chance-constrained programming with joint constraints \|journal=Operations Research \|date=1965 \|volume=13 \|issue=6 \|pages=930-945 \|doi=10.1287/opre.13.6.930}}</ref> CCP is widely used in various fields, including [[finance]], [[engineering]], and [[operations research]], to optimize decision-making processes where certain constraints need to be satisfied with a specified probability.		'''Chance Constrained Programming (CCP)''' is a [[mathematical optimization]] approach used to handle problems under uncertainty. It was first introduced by [[Abraham Charnes\|Charnes]] and [[William W. Cooper\|Cooper]] in 1959 and further developed by Miller and Wagner in 1965.<ref>{{cite journal \|last1=Charnes \|first1=Abraham \|last2=Cooper \|first2=William W. \|title=Chance-Constrained Programming \|journal=Management Science \|date=1959 \|volume=6 \|issue=1 \|pages=73-79 \|doi=10.1287/mnsc.6.1.73}}</ref><ref>{{cite journal \|last1=Miller \|first1=L. R. \|last2=Wagner \|first2=H. M. \|title=Chance-constrained programming with joint constraints \|journal=Operations Research \|date=1965 \|volume=13 \|issue=6 \|pages=930-945 \|doi=10.1287/opre.13.6.930}}</ref> CCP is widely used in various fields, including [[finance]], [[engineering]], and [[operations research]], to optimize decision-making processes where certain constraints need to be satisfied with a specified probability.

	== Theoretical Background ==		== Theoretical Background ==
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	== Practical Applications ==		== Practical Applications ==

	Chance constrained programming is used in engineering for process optimisation under uncertainty and production planning and in finance for for portfolio selection.<ref name=pu/> It has been applied to generating flight trajectory for [[UAV]]s,<ref>{{cite book \|last1=Chai \|first1=Runqi \|title=Advanced Trajectory Optimization, Guidance and Control Strategies for Aerospace Vehicles \|date=2023 \|publisher=Springer Nature Singapore \|isbn=9789819943111 \|page=131}}</ref> and robotic space exploration.<ref>{{cite journal \|last1=Ono \|first1=Masahiro \|last2=Pavone \|first2=Marco \|last3=Kuwata \|first3=Yoshiaki \|last4=Balaram \|first4=J. \|title=Chance-constrained dynamic programming with application to risk-aware robotic space exploration \|journal=Autonomous Robots \|date=2015 \|volume=39 \|pages=555-571 \|doi=10.1007/s10514-015-9467-7}}</ref>		Chance constrained programming is used in engineering for process optimisation under uncertainty and production planning and in finance for for portfolio selection.<ref name=pu/> It has been applied to [[renewable energy]] integration,<ref>{{cite book \|last1=Zhang \|first1=Ning \|last2=Kang \|first2=Chongqing \|last3=Du \|first3=Ershun \|last4=Wang \|first4=Yi \|title=Analytics and Optimization for Renewable Energy Integration \|date=2019 \|publisher=CRC Press \|isbn=9780429847707 \|page=180}}</ref> generating flight trajectory for [[UAV]]s,<ref>{{cite book \|last1=Chai \|first1=Runqi \|title=Advanced Trajectory Optimization, Guidance and Control Strategies for Aerospace Vehicles \|date=2023 \|publisher=Springer Nature Singapore \|isbn=9789819943111 \|page=131}}</ref> and robotic space exploration.<ref>{{cite journal \|last1=Ono \|first1=Masahiro \|last2=Pavone \|first2=Marco \|last3=Kuwata \|first3=Yoshiaki \|last4=Balaram \|first4=J. \|title=Chance-constrained dynamic programming with application to risk-aware robotic space exploration \|journal=Autonomous Robots \|date=2015 \|volume=39 \|pages=555-571 \|doi=10.1007/s10514-015-9467-7}}</ref>

	=== Process Optimization Under Uncertainty ===		=== Process Optimization Under Uncertainty ===

Alaexis: /* Practical Applications */

2024-08-07T12:56:14Z

Practical Applications

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	== Practical Applications ==		== Practical Applications ==

			Chance constrained programming is used in engineering for process optimisation under uncertainty and production planning and in finance for for portfolio selection.<ref name=pu/> It has been applied to generating flight trajectory for [[UAV]]s,<ref>{{cite book \|last1=Chai \|first1=Runqi \|title=Advanced Trajectory Optimization, Guidance and Control Strategies for Aerospace Vehicles \|date=2023 \|publisher=Springer Nature Singapore \|isbn=9789819943111 \|page=131}}</ref> and robotic space exploration.<ref>{{cite journal \|last1=Ono \|first1=Masahiro \|last2=Pavone \|first2=Marco \|last3=Kuwata \|first3=Yoshiaki \|last4=Balaram \|first4=J. \|title=Chance-constrained dynamic programming with application to risk-aware robotic space exploration \|journal=Autonomous Robots \|date=2015 \|volume=39 \|pages=555-571 \|doi=10.1007/s10514-015-9467-7}}</ref>

	=== Process Optimization Under Uncertainty ===		=== Process Optimization Under Uncertainty ===

Alaexis: /* top */

2024-08-05T19:44:57Z

top

← Previous revision		Revision as of 19:44, 5 August 2024
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	'''Chance Constrained Programming (CCP)''' is a mathematical optimization technique used to handle problems under uncertainty. It was first introduced by [[Abraham Charnes\|Charnes]] and [[William W. Cooper\|Cooper]] in 1959 and further developed by Miller and Wagner in 1965.<ref>{{cite journal \|last1=Charnes \|first1=Abraham \|last2=Cooper \|first2=William W. \|title=Chance-Constrained Programming \|journal=Management Science \|date=1959 \|volume=6 \|issue=1 \|pages=73-79 \|doi=10.1287/mnsc.6.1.73}}</ref><ref>{{cite journal \|last1=Miller \|first1=L. R. \|last2=Wagner \|first2=H. M. \|title=Chance-constrained programming with joint constraints \|journal=Operations Research \|date=1965 \|volume=13 \|issue=6 \|pages=930-945 \|doi=10.1287/opre.13.6.930}}</ref> CCP is widely used in various fields, including [[finance]], [[engineering]], and [[operations research]], to optimize decision-making processes where certain constraints need to be satisfied with a specified probability.		'''Chance Constrained Programming (CCP)''' is a [[mathematical optimization]] technique used to handle problems under uncertainty. It was first introduced by [[Abraham Charnes\|Charnes]] and [[William W. Cooper\|Cooper]] in 1959 and further developed by Miller and Wagner in 1965.<ref>{{cite journal \|last1=Charnes \|first1=Abraham \|last2=Cooper \|first2=William W. \|title=Chance-Constrained Programming \|journal=Management Science \|date=1959 \|volume=6 \|issue=1 \|pages=73-79 \|doi=10.1287/mnsc.6.1.73}}</ref><ref>{{cite journal \|last1=Miller \|first1=L. R. \|last2=Wagner \|first2=H. M. \|title=Chance-constrained programming with joint constraints \|journal=Operations Research \|date=1965 \|volume=13 \|issue=6 \|pages=930-945 \|doi=10.1287/opre.13.6.930}}</ref> CCP is widely used in various fields, including [[finance]], [[engineering]], and [[operations research]], to optimize decision-making processes where certain constraints need to be satisfied with a specified probability.

	== Theoretical Background ==		== Theoretical Background ==