Underground nuclear testing - Revision history

31.200.128.116: /* See also */ Books section added

2014-10-16T03:36:33Z

en>Peter Chastain: Clarify that Rongerik and Rongelap are atolls; wikilinks

2014-02-04T08:46:14Z

Clarify that Rongerik and Rongelap are atolls; wikilinks

← Older revision		Revision as of 10:46, 4 February 2014
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	~~'''Penalty methods''' are a certain class of~~ [~~[algorithm]]s for solving [[Constraint (mathematics)\|constrained]] [[optimization (mathematics)\|optimization]] problems~~.		Hello buddy. Allow me extended car [http://blog.Caranddriver.com/buying-peace-of-mind-how-to-buy-a-used-car-warranty/ warranty introduce] myself. I am Luther Aubrey. Bookkeeping is what I [http://livejasminbook.com/index.php?do=/profile-59346/info/ extended auto warranty] do for a residing. Her husband and her [http://Www.consumerreports.org/cro/magazine/2014/04/extended-warranties-for-cars-are-an-expensive-game/ selected] to reside in Delaware but she requirements to transfer simply because of her family. [http://www.vegan-victory.de/index/users/view/id/5378 extended auto warranty] The thing I adore most bottle tops collecting and now I have time to car [http://autos.Jdpower.com/content/buying-tip/xa345A7/pros-and-cons-of-buying-an-extended-warranty-for-a-car.htm warranty] consider on new issues.<br><br>Also visit my blog; [http://Freebusinesscollege.com//read_blog/198199/great-ideas-about-auto-repair-that-anyone-can-use freebusinesscollege.com]

	~~A penalty method replaces a constrained optimization problem by a series~~ of ~~unconstrained problems whose solutions ideally converge~~ to ~~the solution of the original constrained problem. The unconstrained problems are formed by adding~~ a ~~term, called a '''penalty function''', to the [[objective function~~]~~] that consists of a ''penalty parameter'' multiplied by a measure of violation of the constraints~~. ~~The measure of violation is nonzero when the constraints are violated and is zero in the region where constraints are not violated.~~

	~~== Example ==~~

	~~Let us say we are solving the following constrained problem:~~
	~~:<math> \min f(\bold x) </math>~~
	~~subject to~~
	~~:<math> c_i(\bold x) \ge 0 ~\forall i \in~~ I. ~~</math>~~

	~~This problem can be solved as a series of unconstrained minimization problems~~
	~~:<math> \min \Phi_k (\bold x) = f (\bold x) + \sigma_k ~ \sum_{i\in~~ I~~} ~ g(c_i(\bold x)) </math>~~
	~~where~~
	:~~<math> g(c_i(\bold x))=\min(0,~c_i(\bold x ))^2. </math>~~

	~~In the above equations, <math> g(c_i(\bold x))<~~/~~math> is the ''penalty function'' while <math>\sigma_k<~~/~~math> are the ''penalty coefficients''~~. ~~In each iteration ''k'' of the method, we increase the penalty coefficient <math>\sigma_k<~~/math> (e.g. by a factor of 10), solve the unconstrained problem and use the solution as the initial guess for the next iteration. Solutions of the successive unconstrained problems will eventually converge to the solution of the original constrained problem.

	=~~= Practical application ==~~

	~~[[Image compression~~]~~] optimization algorithms can make use of penalty functions~~ for ~~selecting how best to compress zones of colour to single representative values~~.<ref>{{cite journal\|last=Galar\|first=M.\|last2=Jurio\|first2=A.\|last3=Lopez-Molina\|first3= C.\|last4=Paternain\|first4= D.\|last5=Sanz\|first5= J.\|last6=Bustince\|first6=H.\|title=Aggregation functions to combine RGB color channels in stereo matching\|journal=Optics Express\|year=2013\|volume=21\|pages=1247-1257}}</ref><ref>{{cite web\|title=Researchers restore image using version containing between 1 and ~~10 percent of information\|url=~~http://~~phys~~.org/~~news~~/~~2013~~-10-~~image~~-~~version~~-~~percent.html\|publisher=Phys.org (Omicron Technology Limited)\|accessdate=26 October 2013}}<~~/~~ref>~~

	~~== Barrier methods ==~~

	~~[[Barrier method (mathematics)\|Barrier method~~]~~]s constitute an alternative class of algorithms for constrained optimization. These methods also add a penalty-like term~~ to ~~the objective function,~~ but ~~in this case the iterates are forced to remain interior to the feasible domain and the barrier is in place~~ to ~~bias the iterates to remain away from the boundary~~ of ~~the feasible region.~~

	~~== See also ==~~
	* [[Barrier function]]
	* [[Interior point method]]
	* [[Augmented Lagrangian method]]

	~~==References==~~
	~~{{reflist}}~~

	~~Smith, Alice E.; Coit David W~~. [http://~~140~~.~~138~~.~~143.31~~/~~teachers~~/~~ycliang~~/~~heuristic%20optimization%20912~~/~~penalty%20function.pdf Penalty functions~~] ~~Handbook of Evolutionary Computation, Section C 5.2. Oxford University Press~~ and ~~Institute of Physics Publishing, 1996.~~

	~~Courant, R.~~ [http://~~www~~.~~ams~~.~~org~~/~~bull~~/~~1943~~-49-~~01/S0002~~-~~9904~~-~~1943~~-~~07818~~-~~4/S0002~~-~~9904~~-~~1943~~-~~07818~~-4.~~pdf Variational methods for the solution of problems of equilibrium and vibrations~~]. ~~Bull. Amer. Math. Soc., 49, 1&ndash~~;~~23, 1943.~~

	~~{{optimization algorithms}}~~
	[~~[Category~~:~~Optimization algorithms and methods]~~]

en>Monkbot: Fix CS1 deprecated date parameter errors

2014-01-31T05:08:25Z

Fix CS1 deprecated date parameter errors

← Older revision		Revision as of 07:08, 31 January 2014
Line 1:		Line 1:
	~~Hello~~, ~~my name~~ is ~~Andrew~~ and ~~my spouse doesn't like it at all~~. ~~Since~~ I ~~was eighteen~~ I'~~ve been operating as~~ a ~~bookkeeper but soon my wife~~ and I will ~~start our personal business~~. ~~Her family members life in Ohio but her husband wants them~~ to ~~transfer~~. ~~What me and my family members adore is~~ to ~~climb but I'm considering on beginning something new.~~<br><br>~~Also visit telephone [~~http://~~c045~~.~~danah~~.co.kr/~~home/index~~.~~php?document_srl~~=~~1356970&mid~~=~~qna good psychic~~] ([http://~~Cspl~~.~~Postech~~.Ac.kr/~~zboard~~/~~Membersonly~~/~~144571 Learn Additional~~]~~) my website ::~~ [http://www.~~zavodpm~~.ru/~~blogs~~/~~glennmusserrvji~~/~~14565~~-~~great~~-~~hobby~~-~~advice~~-~~assist~~-~~allow~~-~~you~~-~~get~~-~~going free psychic~~]		'''Penalty methods''' are a certain class of [[algorithm]]s for solving [[Constraint (mathematics)\|constrained]] [[optimization (mathematics)\|optimization]] problems.

			A penalty method replaces a constrained optimization problem by a series of unconstrained problems whose solutions ideally converge to the solution of the original constrained problem. The unconstrained problems are formed by adding a term, called a '''penalty function''', to the [[objective function]] that consists of a ''penalty parameter'' multiplied by a measure of violation of the constraints. The measure of violation is nonzero when the constraints are violated and is zero in the region where constraints are not violated.

			== Example ==

			Let us say we are solving the following constrained problem:
			:<math> \min f(\bold x) </math>
			subject to
			:<math> c_i(\bold x) \ge 0 ~\forall i \in I. </math>

			This problem can be solved as a series of unconstrained minimization problems
			:<math> \min \Phi_k (\bold x) = f (\bold x) + \sigma_k ~ \sum_{i\in I} ~ g(c_i(\bold x)) </math>
			where
			:<math> g(c_i(\bold x))=\min(0,~c_i(\bold x ))^2. </math>

			In the above equations, <math> g(c_i(\bold x))</math> is the ''penalty function'' while <math>\sigma_k</math> are the ''penalty coefficients''. In each iteration ''k'' of the method, we increase the penalty coefficient <math>\sigma_k</math> (e.g. by a factor of 10), solve the unconstrained problem and use the solution as the initial guess for the next iteration. Solutions of the successive unconstrained problems will eventually converge to the solution of the original constrained problem.

			== Practical application ==

			[[Image compression]] optimization algorithms can make use of penalty functions for selecting how best to compress zones of colour to single representative values.<ref>{{cite journal\|last=Galar\|first=M.\|last2=Jurio\|first2=A.\|last3=Lopez-Molina\|first3= C.\|last4=Paternain\|first4= D.\|last5=Sanz\|first5= J.\|last6=Bustince\|first6=H.\|title=Aggregation functions to combine RGB color channels in stereo matching\|journal=Optics Express\|year=2013\|volume=21\|pages=1247-1257}}</ref><ref>{{cite web\|title=Researchers restore image using version containing between 1 and 10 percent of information\|url=http://phys.org/news/2013-10-image-version-percent.html\|publisher=Phys.org (Omicron Technology Limited)\|accessdate=26 October 2013}}</ref>

			== Barrier methods ==

			[[Barrier method (mathematics)\|Barrier method]]s constitute an alternative class of algorithms for constrained optimization. These methods also add a penalty-like term to the objective function, but in this case the iterates are forced to remain interior to the feasible domain and the barrier is in place to bias the iterates to remain away from the boundary of the feasible region.

			== See also ==
			* [[Barrier function]]
			* [[Interior point method]]
			* [[Augmented Lagrangian method]]

			==References==
			{{reflist}}

			Smith, Alice E.; Coit David W. [http://140.138.143.31/teachers/ycliang/heuristic%20optimization%20912/penalty%20function.pdf Penalty functions] Handbook of Evolutionary Computation, Section C 5.2. Oxford University Press and Institute of Physics Publishing, 1996.

			Courant, R. [http://www.ams.org/bull/1943-49-01/S0002-9904-1943-07818-4/S0002-9904-1943-07818-4.pdf Variational methods for the solution of problems of equilibrium and vibrations]. Bull. Amer. Math. Soc., 49, 1–23, 1943.

			{{optimization algorithms}}
			[[Category:Optimization algorithms and methods]]

en>TestBanNow: /* International treaties */ Update Annex 2 States (Indonesia)

2012-05-29T13:19:57Z

International treaties: Update Annex 2 States (Indonesia)

New page

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