Codex Athous Lavrensis - Revision history

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2015-01-11T12:08:25Z

← Older revision		Revision as of 14:08, 11 January 2015
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	~~{{dablink\|This article is related~~ to ~~[[mathematical programming]]~~. ~~For other uses see [[complementarity (disambiguation)\|complementarity]].}}~~		Please read on to find out more about injury legislation. When moving the right path by means of accidental injuries rules, you're not just likely to need the correct information and facts on your own, but you're gonna want a great personal injury legal representative. Do you wish to capture from the trendy and expect for the very best, or can you instead prepare yourself?<br><br>When writing down what happened following a car accident, you should details your traumas plainly. If you have any type of concerns relating to where and ways to use [https://app.box.com/services/box_notes/2133/21574687741/d38606.f3fa3250404d1b38622d390a0a372615bc30de78b658cde4cb39431e2d17f123?from_https=1&shared_name=5ntl83jid4zk9ragqlk8 accidental injury Endorsement], you can contact us at our web-site. 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	A ''~~'complementarity problem''' is~~ a ~~type of [[mathematical optimization]] problem~~. ~~It is~~ the ~~problem of optimizing (minimizing~~ or ~~maximizing)~~ a ~~function~~ of ~~two~~ [~~[vector space\|vector~~]~~] variables subject~~ to ~~certain requirements (constraints) which include: that~~ the ~~[[inner product]] of~~ the ~~two vectors must equal zero~~, i.e. ~~orthoginal~~.<~~ref~~>~~{{Cite journal \| last1=Billups \| first1=Stephen \| last2=Murty \| first2=Katta \| title=Complementarity Problems \| doi=10~~.~~1016/S0377-0427(00)00432-5\|url=~~http://www~~-personal~~.~~umich~~.~~edu~~/~~~murty/LCPart~~.~~ps \| year=2000 \| journal=Journal of Computational and Applied Mathematics \| volume=124 \| pages=303}}~~ <~~/ref~~> In ~~particular for finite-dimensional real vector spaces~~ this ~~means that~~, ~~if one has vectors ''X'' and ''Y''~~ with ~~''nonnegative'' components (''x''~~<~~sub~~>~~''i''~~<~~/sub~~>~~ ≥ 0~~ and ~~''y''~~<~~sub~~>~~''i''~~<~~/sub~~>~~ ≥ 0 for all~~ <~~math~~>i<~~/math~~>~~: in~~ the ~~[[first quadrant]] if 2-dimensional~~, in the ~~first [[octant (solid geometry)\|octant]] if 3-dimensional)~~, ~~then for each pair of components ''x''~~<~~sub~~>~~''i''~~</~~sub>~~ and ~~''y''~~<~~sub~~>~~''i''~~<~~/sub~~> ~~one~~ of the ~~pair must~~ be ~~zero, hence~~ the ~~name ''complementarity''~~. ~~e.g. ''X'' = (1~~,~~ 0) and~~ '~~'Y'' = (0, 2)~~ are ~~complementary~~, ~~but ''X'' = (1~~,~~ 1) and ''Y'' = (2~~,~~ 0) are not. A complementarity problem~~ is ~~a special case of a [[variational inequality]]~~.

	~~==History==~~
	~~Complementarity problems were originally studied because~~ the ~~[[Karush–Kuhn–Tucker conditions]] in [[linear programming]]~~ and ~~[[quadratic programming]] constitute a [[linear complementarity problem]] (LCP)~~ or ~~a [[mixed complementarity problem]] (MCP)~~. ~~In 1963 [[Carlton E~~. ~~Lemke\|Lemke]] and [[J.T. Howson\|Howson]] showed that,~~ for ~~two person games, computing a [[Nash equilibrium]] point~~ is ~~equivalent~~ to ~~an LCP~~. In ~~1968 [[Richard W. Cottle\|Cottle]] and [[George B. Dantzig\|Dantzig]] unified linear and quadratic programming and [[bimatrix game]]s~~. ~~Since then~~ the ~~study of complementarity problems and variational inequalities has expanded enormously.~~

	~~Areas~~ of ~~[[mathematics]] and [[science]] that contributed to the development~~ of ~~complementarity theory~~
	~~include: [[Optimization (mathematics)\|optimization]]~~, ~~[[equilibrium point\|equilibrium]] problems, [[Variational inequality\|variational inequality theory]], [[fixed point theory]], [[topological degree theory]] and [[nonlinear analysis]]~~.

	~~==See also==~~
	* [[Mathematical programming with equilibrium constraints]]
	* [[nl (format)\|nl format]] for representing complementarity problems

	~~==References==~~
	<~~references/~~>

	~~==Further reading==~~

	* {{cite book \| author=Richard W. ~~Cottle~~, ~~Jong-Shi Pang~~, ~~Richard E~~. ~~Stone \| title=The Linear Complementarity Problem~~
	~~\| publisher=Academic Press \| year=1992 \| isbn=978-0-12-192350-1}}~~
	* {{cite book \| author=George Isac \| title=Complementarity Problems \| publisher=Springer \| year=1992 \| isbn=978-3-540-56251-1}}
	* {{cite book \| author=George Isac \| title=Topological Methods in ~~Complementarity Theory \| publisher=Springer \| year=2000 \| isbn=978-0-7923-6274-6}}~~
	* {{cite book \| author=Francisco Facchinei, ~~Jong-Shi Pang \| title=Finite-Dimensional Variational Inequalities and Complementarity Problems: v~~.1 and v.~~2 \| publisher=Springer \| year=2003 \| isbn=978-0-387-95580-3}}~~
	* {{cite book \|last=Murty \|first=K. G. \|title=Linear complementarity, ~~linear~~ and ~~nonlinear programming \|series=Sigma Series~~ in ~~Applied Mathematics \|volume=3 \|publisher=Heldermann Verlag \|location=Berlin \|year=1988 \|pages=xlviii+629 pp. \|isbn=3-88538-403-5 \|url=http://ioe.engin.umich~~.~~edu/people/fac/books/murty/linear_complementarity_webbook/ \|mr=949214}}~~

	~~===Collections===~~

	* {{cite book \| editor=Richard Cottle, ~~F. Giannessi~~, ~~Jacques Louis Lions \| title=Variational Inequalities and Complementarity Problems: Theory and Applications \| publisher=John Wiley & Sons \| year=1980 \| isbn=978-0-471-27610-4}}~~
	* {{cite book \| editor=Michael C. ~~Ferris, Jong-Shi Pang \| title=Complementarity and Variational Problems: State~~ of ~~the Art \| publisher=SIAM \| year=1997 \| isbn=978-0-89871-391-6}}~~

	~~==External links==~~
	*[http://www.cs.~~wisc.edu/cpnet/ CPNET:Complementarity Problem Net]{{Dead link\|date=May 2013}}~~

	~~[[Category:Mathematical optimization]]~~
	~~[[Category:Functional analysis]]~~
	~~[[Category:Topology]]~~
	~~[[Category:Numerical analysis]]~~


	~~{{mathanalysis-stub}}~~

en>Leszek Jańczuk: ref

2013-03-16T13:08:40Z

ref

← Older revision		Revision as of 15:08, 16 March 2013
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	~~2 Leo may be the name mother and father gave me and I totally love this nickname~~. ~~Some time ago I chosen to live in North Dakota~~. ~~The job I~~'~~ve been occupying hottest~~ is ~~an accounting officer but I've always wanted~~ a ~~business~~. ~~Acting~~ is ~~something~~ that ~~she's been doing widespread beverages~~ .. ~~See what's new on my website here: https~~://www.~~youtube~~.~~com~~/~~watch?v~~=~~kKqUUeVzoLE~~<br><br>~~Feel free~~ to ~~visit my weblog~~: ~~online treatment for social anxiety~~ ([~~https~~://~~www~~.~~youtube~~.~~com~~/~~watch?v~~=~~kKqUUeVzoLE Going to~~ www.~~youtube~~.~~com~~])		{{dablink\|This article is related to [[mathematical programming]]. For other uses see [[complementarity (disambiguation)\|complementarity]].}}

			A '''complementarity problem''' is a type of [[mathematical optimization]] problem. It is the problem of optimizing (minimizing or maximizing) a function of two [[vector space\|vector]] variables subject to certain requirements (constraints) which include: that the [[inner product]] of the two vectors must equal zero, i.e. orthoginal.<ref>{{Cite journal \| last1=Billups \| first1=Stephen \| last2=Murty \| first2=Katta \| title=Complementarity Problems \| doi=10.1016/S0377-0427(00)00432-5\|url=http://www-personal.umich.edu/~murty/LCPart.ps \| year=2000 \| journal=Journal of Computational and Applied Mathematics \| volume=124 \| pages=303}} </ref> In particular for finite-dimensional real vector spaces this means that, if one has vectors ''X'' and ''Y'' with ''nonnegative'' components (''x''<sub>''i''</sub> ≥ 0 and ''y''<sub>''i''</sub> ≥ 0 for all <math>i</math>: in the [[first quadrant]] if 2-dimensional, in the first [[octant (solid geometry)\|octant]] if 3-dimensional), then for each pair of components ''x''<sub>''i''</sub> and ''y''<sub>''i''</sub> one of the pair must be zero, hence the name ''complementarity''. e.g. ''X'' = (1, 0) and ''Y'' = (0, 2) are complementary, but ''X'' = (1, 1) and ''Y'' = (2, 0) are not. A complementarity problem is a special case of a [[variational inequality]].

			==History==
			Complementarity problems were originally studied because the [[Karush–Kuhn–Tucker conditions]] in [[linear programming]] and [[quadratic programming]] constitute a [[linear complementarity problem]] (LCP) or a [[mixed complementarity problem]] (MCP). In 1963 [[Carlton E. Lemke\|Lemke]] and [[J.T. Howson\|Howson]] showed that, for two person games, computing a [[Nash equilibrium]] point is equivalent to an LCP. In 1968 [[Richard W. Cottle\|Cottle]] and [[George B. Dantzig\|Dantzig]] unified linear and quadratic programming and [[bimatrix game]]s. Since then the study of complementarity problems and variational inequalities has expanded enormously.

			Areas of [[mathematics]] and [[science]] that contributed to the development of complementarity theory
			include: [[Optimization (mathematics)\|optimization]], [[equilibrium point\|equilibrium]] problems, [[Variational inequality\|variational inequality theory]], [[fixed point theory]], [[topological degree theory]] and [[nonlinear analysis]].

			==See also==
			* [[Mathematical programming with equilibrium constraints]]
			* [[nl (format)\|nl format]] for representing complementarity problems

			==References==
			<references/>

			==Further reading==

			* {{cite book \| author=Richard W. Cottle, Jong-Shi Pang, Richard E. Stone \| title=The Linear Complementarity Problem
			\| publisher=Academic Press \| year=1992 \| isbn=978-0-12-192350-1}}
			* {{cite book \| author=George Isac \| title=Complementarity Problems \| publisher=Springer \| year=1992 \| isbn=978-3-540-56251-1}}
			* {{cite book \| author=George Isac \| title=Topological Methods in Complementarity Theory \| publisher=Springer \| year=2000 \| isbn=978-0-7923-6274-6}}
			* {{cite book \| author=Francisco Facchinei, Jong-Shi Pang \| title=Finite-Dimensional Variational Inequalities and Complementarity Problems: v.1 and v.2 \| publisher=Springer \| year=2003 \| isbn=978-0-387-95580-3}}
			* {{cite book \|last=Murty \|first=K. G. \|title=Linear complementarity, linear and nonlinear programming \|series=Sigma Series in Applied Mathematics \|volume=3 \|publisher=Heldermann Verlag \|location=Berlin \|year=1988 \|pages=xlviii+629 pp. \|isbn=3-88538-403-5 \|url=http://ioe.engin.umich.edu/people/fac/books/murty/linear_complementarity_webbook/ \|mr=949214}}

			===Collections===

			* {{cite book \| editor=Richard Cottle, F. Giannessi, Jacques Louis Lions \| title=Variational Inequalities and Complementarity Problems: Theory and Applications \| publisher=John Wiley & Sons \| year=1980 \| isbn=978-0-471-27610-4}}
			* {{cite book \| editor=Michael C. Ferris, Jong-Shi Pang \| title=Complementarity and Variational Problems: State of the Art \| publisher=SIAM \| year=1997 \| isbn=978-0-89871-391-6}}

			==External links==
			*[http://www.cs.wisc.edu/cpnet/ CPNET:Complementarity Problem Net]{{Dead link\|date=May 2013}}

			[[Category:Mathematical optimization]]
			[[Category:Functional analysis]]
			[[Category:Topology]]
			[[Category:Numerical analysis]]


			{{mathanalysis-stub}}

en>Davidiad: /* Text */clean up, replaced: {{Polytonic| → {{lang|grc| using AWB

2012-04-21T17:13:34Z

Text: clean up, replaced: {{Polytonic| → {{lang|grc| using AWB

New page

2 Leo may be the name mother and father gave me and I totally love this nickname. Some time ago I chosen to live in North Dakota. The job I've been occupying hottest is an accounting officer but I've always wanted a business. Acting is something that she's been doing widespread beverages .. See what's new on my website here: https://www.youtube.com/watch?v=kKqUUeVzoLE<br><br>Feel free to visit my weblog: online treatment for social anxiety ([https://www.youtube.com/watch?v=kKqUUeVzoLE Going to www.youtube.com])