Neural decoding - Revision history

en>564dude: Added {{open access}} for references from PLoS journals

2014-11-10T00:11:40Z

Added {{open access}} for references from PLoS journals

← Older revision		Revision as of 02:11, 10 November 2014
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	~~My name is Santiago (49 years old)~~ and ~~my hobbies~~ are ~~Camping~~ and ~~Vintage car~~.<br><br>~~Visit my blog: [http://tinyurl~~.~~com/q6d8aya Cheap ghd uk]~~		Simple Methods to Keep Your Stainless Steel Refrigerators Clean<br><br>

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en>Monkbot: Fix CS1 deprecated date parameter errors

2014-02-10T01:20:37Z

Fix CS1 deprecated date parameter errors

← Older revision		Revision as of 03:20, 10 February 2014
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	~~{{confusing\|date=October 2011}}~~		My name is Santiago (49 years old) and my hobbies are Camping and Vintage car.<br><br>Visit my blog: [http://tinyurl.com/q6d8aya Cheap ghd uk]
	~~{{technical\|date=October 2011}}~~
	In [[mathematics]], '''Slater's condition''' (or '''Slater condition''') is a [[sufficient condition]] for [[strong duality]] to hold for a [[convex optimization\|convex optimization problem]]. This is a specific example of a [[constraint qualification]]. In particular, if Slater's condition holds for the [[primal problem]], then the [[duality gap]] is 0, and if the dual value is finite then it is attained.<ref>{{cite book \|last1=Borwein \|first1=Jonathan \|last2=Lewis \|first2=Adrian \|title=Convex Analysis and Nonlinear Optimization: Theory and Examples\| edition=2 \|year=2006 \|publisher=Springer \|isbn=978-0-387-29570-1}}</ref>

	~~==Mathematics==~~
	~~Given the problem~~
	~~:<math> \text{Minimize }\; f_0~~(x) ~~</math>~~
	~~:<math> \text{subject to: }\ </math>~~
	~~::<math> f_i(x) \le 0 , i = 1,\ldots,m</math>~~
	~~::<math> Ax = b</math>~~
	~~with <math>f_0,\ldots,f_m</math> [[convex function\|convex]] (~~and therefore a convex optimization problem). Then Slater's condition implies that strong duality holds if there exists an <math>x \in \operatorname{relint}(D)</math> (where relint is the [[relative interior]] and <math>D = \cap_{i = 0}^m \operatorname{dom}(f_i)</math>) such that
	~~:<math>f_i(x) < 0, i = 1,\ldots,m</math>~~ and
	~~:<math>Ax = b~~.\,<~~/math~~><~~ref name="boyd"~~>~~{{cite book \|last1=Boyd \|first1=Stephen \|last2=Vandenberghe \|first2=Lieven \|title=Convex Optimization \|publisher=Cambridge University Press \|year=2004 \|isbn=978-0-521-83378-3 \|url=http~~:~~//www.stanford.edu/~boyd/cvxbook/bv_cvxbook.pdf \|format=pdf \|accessdate=October 3, 2011}}</ref>~~

	~~If the first <math>k</math> constraints, <math>f_1,\ldots,f_k</math> are~~ [~~[linear function]]s, then strong duality holds if there exists an <math>x \in \operatorname{relint}(D)</math> such that~~
	~~:<math>f_i(x) \le 0, i = 1,\ldots,k,</math>~~
	~~:<math>f_i(x) < 0, i = k+1,\ldots,m,</math> and~~
	~~:<math>Ax = b.\,</math><ref name="boyd" />~~

	~~===Generalized Inequalities===~~
	~~Given the problem~~
	~~:<math> \text{Minimize }\; f_0(x) </math>~~
	~~:<math> \text{subject to: }\ </math>~~
	~~::<math> f_i(x) \le_{K_i} 0 , i = 1,\ldots,m</math>~~
	~~::<math> Ax = b</math>~~
	where <math>f_0</math> is convex and <math>f_i</math> is <math>K_i</math>-convex for each <math>i</math>. Then Slater's condition says that if there exists an <math>x \in \operatorname{relint}(D)</math> such that
	:~~<math>f_i(x) <_{K_i} 0, i = 1,\ldots,m<~~/~~math> and~~
	~~:<math>Ax = b<~~/~~math>~~
	~~then strong duality holds~~.~~<ref name="boyd"~~ />

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

	~~[[Category:Mathematical optimization]~~]

en>Wikiscottcha: /* Spike train number */ typo "in" -> "is"

2013-10-15T04:16:47Z

Spike train number: typo "in" -> "is"

@@ Line 1: / Line 1: @@
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+{{confusing|date=October 2011}}
-目にする必要があり、
+{{technical|date=October 2011}}
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+In [[mathematics]], '''Slater's condition''' (or '''Slater condition''') is a [[sufficient condition]] for [[strong duality]] to hold for a [[convex optimization|convex optimization problem]].  This is a specific example of a [[constraint qualification]].  In particular, if Slater's condition holds for the [[primal problem]], then the [[duality gap]] is 0, and if the dual value is finite then it is attained.<ref>{{cite book |last1=Borwein |first1=Jonathan |last2=Lewis |first2=Adrian |title=Convex Analysis and Nonlinear Optimization: Theory and Examples| edition=2 |year=2006 |publisher=Springer |isbn=978-0-387-29570-1}}</ref>
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+==Mathematics==

en>Rjwilmsi: Format plain DOIs using AWB (8060)

2012-04-10T17:42:03Z

Format plain DOIs using AWB (8060)

New page

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