Mathematical optimization - Revision history

128.112.66.66 at 13:38, 2 January 2015

2015-01-02T13:38:18Z

en>Limit-theorem: clearer as optimization often associated with constraints rather than domain.

2014-03-02T19:13:47Z

clearer as optimization often associated with constraints rather than domain.

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	~~[[Image:Gabriel~~-~~Lamé~~.~~jpeg\|thumb\|Gabriel Lamé]]~~
	~~'''Gabriel Léon Jean Baptiste Lamé''' (22 July 1795 – 1 May 1870) was a French mathematician who contributed~~ to the ~~theory~~ of ~~partial differential equations by the use~~ of ~~curvilinear coordinates, and~~ the ~~mathematical theory of elasticity~~.

	~~==Biography==~~
	~~Lamé was born in [[Tours]]~~, ~~in today's ''département'' of [[Indre-et-Loire]].~~

	~~He became well known for his general theory~~ of ~~[[curvilinear coordinates]] and his notation and study of classes of ellipse~~-~~like curves, now known as~~ [~~[Lamé curve]]s or superellipses, and defined by the equation~~:

	~~: <math> \left\|\,{x\over a}\,\right\|^n + \left\|\,{y\over b}\,\right\|^n =1 <~~/~~math>~~

	~~where ''n'' is any positive [[real number]]~~.

	~~He is also known for his [[running time]] analysis of the [[Euclidean algorithm]~~], ~~marking~~ the ~~beginning of [[computational complexity theory]]~~. ~~Using [[Fibonacci number]]s, he proved~~ that ~~when finding~~ the ~~[[greatest common divisor]] of integers ''a'' and ''b''~~, the ~~algorithm runs~~ in ~~no more than 5''k'' steps, where ''k'' is~~ the ~~number of (decimal) [[numerical digit\|digit]]s of ''b''~~. ~~He also proved a special case of [[Fermat's last theorem]]. He actually thought that he found a complete proof for the theorem~~, ~~but his proof was flawed.~~
	~~The [[Lamé function]]s~~ are ~~part of~~ the ~~theory~~ of ~~[[ellipsoidal harmonic]]s.~~

	~~He worked on a wide variety~~ of ~~different topics~~. ~~Often problems~~ in the ~~engineering tasks he undertook led him to study mathematical questions~~. ~~For example his~~ work on the ~~stability~~ of ~~vaults and on the design of suspension bridges led him~~ to ~~work on elasticity theory. In fact this was not a passing interest~~, ~~for Lamé made substantial contributions~~ to ~~this topic~~. ~~Another example is his work on the conduction~~ of ~~heat which led him to his theory of curvilinear coordinates~~.

	~~Curvilinear coordinates proved a very powerful tool~~ in ~~Lamé's hands. He used them~~ to ~~transform Laplace's equation into ellipsoidal coordinates~~ and ~~so separate~~ the ~~variables and solve~~ the ~~resulting equation~~.

	~~His most significant contribution~~ to ~~engineering was to accurately define the stresses and capabilities of a press fit joint, such as that seen in~~ a ~~dowel pin~~ in ~~a housing.~~

	~~In 1854~~, ~~he was elected a foreign member of~~ the ~~[[Royal Swedish Academy of Sciences]].~~

	~~Lamé died~~ in ~~[[Paris]] in 1870~~. ~~His name is~~ one ~~of the [[List of the 72 names on the Eiffel Tower\|72 names inscribed on the Eiffel Tower]].~~

	~~==Books by G. Lamé==~~
	* [http://gallica.bnf.fr/notice?N=FRBNF37268127 Leçons sur les coordonnées curvilignes et leurs diverses applications] (Mallet-Bachelier, ~~1859)~~
	* [http://~~gallica.bnf~~.fr/~~notice?N=FRBNF37259502 Leçons sur les fonctions inverses des transcendantes et les surfaces isothermes ] (Mallet-Bachelier, 1857)~~
	* [http://gallica.bnf.fr/~~notice?N=FRBNF38827934 Leçons sur la théorie analytique de la chaleur] (Mallet~~-~~Bachelier, 1861)~~
	* [http:/~~/gallica.bnf.fr/notice~~?N=~~FRBNF37259227 Examen des différentes méthodes employées pour résoudre les problèmes de géométrie~~ ] ~~( Vve Courcier, 1818)~~
	* [http://gallica.~~bnf.fr/notice?N=FRBNF37277624 Cours de physique de l~~'~~Ecole Polytechnique~~. ~~Tome premier, Propriétés générales des corps—Théorie physique de la chaleur] (Bachelier, 1840)~~
	* [http://gallica.~~bnf.fr/notice?N=FRBNF37284136 Cours de physique de l'Ecole Polytechnique. Tome deuxième~~, ~~Acoustique—Théorie physique de la lumière] (Bachelier, 1840)~~
	* [http://gallica.~~bnf~~.~~fr/notice?N=FRBNF37284138 Cours de physique de l'Ecole Polytechnique~~. ~~Tome troisième, Electricité-Magnétisme-Courants électriques-Radiations] (Bachelier, 1840)~~
	* [http://books.google.com/books?id=rat4N6-k_QcC&pg=RA1-PR10&dq=Gabriel+Lam%C3%A9&hl=fr#PRA1-PR3,M1 Leçons sur la théorie mathématique de l'élasticité des corps solides] (Bachelier, 1852)

	~~==See also==~~
	* [[Lamé crater]]
	* [[Piet Hein (Denmark)\|Piet Hein]]
	* [[Lamé's ~~special quartic]]~~
	* [[Julius Plücker]]
	* [[Stefan problem]]
	* [[Super ellipse]]
	* [[Lamé parameters]]

	~~==External links==~~
	* [http://mathworld.~~wolfram.com/Superellipse.html Superellipse~~ (~~MathWorld)]~~
	* [http://~~www~~.~~activeart~~.~~de/dim-shops/training/SuperEllipse Lamé~~'s ~~Oval / Superellipse (Java-applet)]~~
	* {{MacTutor Biography\|id=Lame}}

	~~{{Authority control\|VIAF=24685200}}~~

	~~{{Persondata <!-- Metadata: see [[Wikipedia:Persondata]]~~. ~~-->~~
	~~\| NAME = Lame~~, ~~Gabriel~~
	~~\| ALTERNATIVE NAMES =~~
	~~\| SHORT DESCRIPTION = French mathematician~~
	~~\| DATE OF BIRTH = 22 July 1795~~
	~~\| PLACE OF BIRTH =~~
	~~\| DATE OF DEATH =~~ 1 ~~May 1870~~
	~~\| PLACE OF DEATH =~~
	}}
	~~{{DEFAULTSORT:Lame, Gabriel}}~~
	~~[[Category:École Polytechnique alumni]]~~
	~~[[Category:Mines ParisTech alumni]]~~
	~~[[Category:Corps des mines]]~~
	~~[[Category:1795 births]]~~
	~~[[Category:1870 deaths]]~~
	~~[[Category:People from Tours]]~~
	~~[[Category:Members of the French Academy of Sciences]]~~
	~~[[Category:Members of the Royal Swedish Academy of Sciences]]~~
	~~[[Category:19th-century French mathematicians]]~~

en>ChrisGualtieri: Checkwiki + General Fixes using AWB

2013-12-22T06:09:38Z

Checkwiki + General Fixes using AWB

Show changes

en>Isheden: /* Iterative methods */ Iterative methods are not mentioned in the article nonlinear programming

2012-08-24T13:36:24Z

Iterative methods: Iterative methods are not mentioned in the article nonlinear programming

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