Riemann Xi function - Revision history

en>LokiClock: /* Series representations */ Converges conditionally

2014-10-14T10:13:03Z

Series representations: Converges conditionally

← Older revision		Revision as of 12:13, 14 October 2014
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	~~In [[convex optimization]], a '''linear matrix inequality''' ('''LMI''')~~ is ~~an expression of the form~~		Hello and welcome. My title is Figures Wunder. My day occupation is a meter reader. One of the extremely best things in the world for me is to do aerobics and now I'm attempting to earn money with it. For many years he's been residing in North Dakota and his family enjoys it.<br><br>Here is my web-site: home std test kit, [http://www.hotporn123.com/user/RPocock Going to www.hotporn123.com],
	~~: <math>\operatorname{LMI}(y):=A_0+y_1A_1+y_2A_2+\cdots+y_m A_m\geq0\,</math>~~
	~~where~~
	* <math>y=[y_i\,,~i\!=\!1,\dots, m]</math> is a ~~real vector,~~
	* <math>A_0, A_1, A_2,\dots,A_m</math> are <math>n\times n</math> [[symmetric matrix \| symmetric matrices]] <math>\mathbb{S}^n</math>,
	* <math>B\geq0 </math> is a generalized inequality meaning <math>B</math> is a [[positive semidefinite matrix]] belonging to the ~~positive semidefinite cone <math>\mathbb{S}_+</math>~~ in the ~~subspace of symmetric matrices <math>\mathbb{S}</math>.~~

	~~This linear matrix inequality specifies a [[convex set\|convex]] constraint on ''y''.~~

	~~== Applications ==~~
	~~There are efficient numerical methods~~ to ~~determine whether an LMI is feasible (~~'~~'e.g.'', whether there exists a vector ''y'' such that LMI(''y'') ≥ 0), or~~ to ~~solve a [[convex optimization]] problem~~ with ~~LMI constraints~~.
	~~Many optimization problems~~ in ~~[[control theory]], [[system identification]]~~ and ~~[[signal processing]] can be formulated using LMIs~~. ~~Also LMIs find application in [[Polynomial SOS\|Polynomial Sum-Of-Squares]]. The prototypical primal and dual [[semidefinite programming\|semidefinite program]]~~ is ~~a minimization of a real linear function respectively subject to the primal and dual [[convex cone]]s governing this LMI.~~

	~~== Solving LMIs ==~~

	~~A major breakthrough in convex optimization lies in the introduction of [[interior~~-~~point method]]s. These methods were developed in a series of papers and became of true interest in the context of LMI problems in the work of Yurii Nesterov and Arkadii Nemirovskii.~~

	~~== References ==~~

	* Y. Nesterov and A. Nemirovsky, ''Interior Point Polynomial Methods in Convex Programming.'' SIAM, 1994.

	~~== External links ==~~
	* S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan, [http://www.~~stanford~~.~~edu/~boyd/lmibook/ Linear Matrix Inequalities in System and Control Theory] (book in pdf)~~

	* C. Scherer and S. Weiland [http://www.~~dcsc.tudelft.nl/~cscherer/lmi~~.~~html Course on Linear Matrix Inequalities in Control~~], ~~Dutch Institute of Systems and Control (DISC).~~

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

en>Sapphorain: Undid revision 590381165 by 173.79.231.84 (talk)

2014-01-12T17:56:16Z

Undid revision 590381165 by 173.79.231.84 (talk)

← Older revision		Revision as of 19:56, 12 January 2014
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	~~Alyson Meagher~~ is the ~~title her parents gave her but she doesn~~'~~t like when people use her complete name~~. ~~For many years she~~'s ~~been working as~~ a ~~journey agent~~. ~~For many years he~~'~~s been living~~ in ~~Alaska and he doesn~~'~~t plan on changing it~~. ~~To climb is something she would by no means give up~~.~~<br><br>Feel free to visit my blog -~~ [http://~~cspl~~.~~postech~~.ac.kr/~~zboard~~/~~Membersonly~~/~~144571 free online tarot card readings~~]		In [[convex optimization]], a '''linear matrix inequality''' ('''LMI''') is an expression of the form
			: <math>\operatorname{LMI}(y):=A_0+y_1A_1+y_2A_2+\cdots+y_m A_m\geq0\,</math>
			where
			* <math>y=[y_i\,,~i\!=\!1,\dots, m]</math> is a real vector,
			* <math>A_0, A_1, A_2,\dots,A_m</math> are <math>n\times n</math> [[symmetric matrix \| symmetric matrices]] <math>\mathbb{S}^n</math>,
			* <math>B\geq0 </math> is a generalized inequality meaning <math>B</math> is a [[positive semidefinite matrix]] belonging to the positive semidefinite cone <math>\mathbb{S}_+</math> in the subspace of symmetric matrices <math>\mathbb{S}</math>.

			This linear matrix inequality specifies a [[convex set\|convex]] constraint on ''y''.

			== Applications ==
			There are efficient numerical methods to determine whether an LMI is feasible (''e.g.'', whether there exists a vector ''y'' such that LMI(''y'') ≥ 0), or to solve a [[convex optimization]] problem with LMI constraints.
			Many optimization problems in [[control theory]], [[system identification]] and [[signal processing]] can be formulated using LMIs. Also LMIs find application in [[Polynomial SOS\|Polynomial Sum-Of-Squares]]. The prototypical primal and dual [[semidefinite programming\|semidefinite program]] is a minimization of a real linear function respectively subject to the primal and dual [[convex cone]]s governing this LMI.

			== Solving LMIs ==

			A major breakthrough in convex optimization lies in the introduction of [[interior-point method]]s. These methods were developed in a series of papers and became of true interest in the context of LMI problems in the work of Yurii Nesterov and Arkadii Nemirovskii.

			== References ==

			* Y. Nesterov and A. Nemirovsky, ''Interior Point Polynomial Methods in Convex Programming.'' SIAM, 1994.

			== External links ==
			* S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan, [http://www.stanford.edu/~boyd/lmibook/ Linear Matrix Inequalities in System and Control Theory] (book in pdf)

			* C. Scherer and S. Weiland [http://www.dcsc.tudelft.nl/~cscherer/lmi.html Course on Linear Matrix Inequalities in Control], Dutch Institute of Systems and Control (DISC).

			[[Category:Mathematical optimization]]

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2012-08-08T22:23:47Z

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Alyson Meagher is the title her parents gave her but she doesn't like when people use her complete name. For many years she's been working as a journey agent. For many years he's been living in Alaska and he doesn't plan on changing it. To climb is something she would by no means give up.<br><br>Feel free to visit my blog - [http://cspl.postech.ac.kr/zboard/Membersonly/144571 free online tarot card readings]