Subgradient method - Revision history

131.152.224.35: /* General constraints */ link to "subdifferential"

2014-10-14T15:04:53Z

General constraints: link to "subdifferential"

← Older revision		Revision as of 17:04, 14 October 2014
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en>Monkbot: /* Subgradient-projection & bundle methods */Fix CS1 deprecated date parameter errors (test)

2014-02-26T16:56:52Z

Subgradient-projection & bundle methods: Fix CS1 deprecated date parameter errors (test)

← Older revision		Revision as of 18:56, 26 February 2014
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	~~{{Unreferenced\|date=March 2007}}~~		Hi there. Allow me start by introducing the writer, her name is Sophia. Distributing production is how he tends to make a living. Mississippi is exactly where her house is but her husband desires them to move. To perform lacross is the thing I adore most of all.<br><br>my webpage [http://www.prayerarmor.com/uncategorized/dont-know-which-kind-of-hobby-to-take-up-read-the-following-tips/ authentic psychic readings]
	~~In [[mathematics]]~~, a ~~complete set of [[Invariant (mathematics)\|invariant]]s for a [[classification theorems\|classification problem]]~~ is ~~a collection of maps~~
	~~:<math>f_i : X \~~to ~~Y_i \,</math>~~
	~~(where ''X''~~ is the ~~collection~~ of ~~objects being classified, up to some equivalence relation, and the~~ <~~math~~>~~Y_i~~<~~/math~~> ~~are some sets), such that <math>x<~~/~~math> ∼ <math>x'<~~/~~math> if and only if <math>f_i(x) = f_i(x')</math> for all ''i''~~. ~~In words, such that two objects are equivalent if and only if all invariants are equal~~.

	~~Symbolically, a complete set of invariants is a collection of maps such that~~
	~~:<math>\prod f_i : (X~~/~~\sim) \to \prod Y_i<~~/~~math>~~
	~~is [[injective]].~~

	~~As invariants are, by definition, equal on equivalent objects, equality~~ of invariants is a ''necessary'' condition for equivalence; a ''complete'' set of invariants is a set such that equality of these is ''sufficient'' for equivalence. In the context of a group action, this may be stated as: invariants are functions of [[coinvariant]]s (equivalence classes, orbits), and a complete set of invariants characterizes the coinvariants (is a set of defining equations for the coinvariants).

	~~==Examples==~~
	* In the [[classification of two-~~dimensional closed manifolds]], [[Euler characteristic]] (or [[Genus (mathematics)\|genus]]) and [[orientability]] are a complete set of invariants.~~
	* [[Jordan normal form]] of a matrix is a complete invariant for matrices up ~~to conjugation, but [[eigenvalue]]s (with multiplicities) are not.~~

	~~==Realizability of invariants==~~
	~~A complete set of invariants does not immediately yield a [[classification theorem]]: not all combinations of invariants may be realized. Symbolically, one must also determine~~ the ~~image of~~
	~~:<math>\prod f_i : X \to \prod Y_i.<~~/~~math>~~

	~~{{DEFAULTSORT:Complete Set Of Invariants}}~~
	~~[[Category:Mathematical terminology]~~]

en>Moritzge: /* Classical subgradient rules */ missing full-stop added

2013-07-30T08:18:16Z

Classical subgradient rules: missing full-stop added

← Older revision		Revision as of 10:18, 30 July 2013
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	~~Nice~~ to ~~satisfy you~~, ~~my title~~ is ~~Refugia~~. ~~To gather coins~~ is ~~what her family and her appreciate~~. ~~Hiring~~ is ~~my profession~~. ~~Puerto Rico~~ is ~~exactly where he~~ and ~~his spouse reside~~.<br><br>~~Visit my homepage -~~ [~~http~~:~~//www.ubi-cation.com/ubication/node/6056 at home std test~~]		{{Unreferenced\|date=March 2007}}
			In [[mathematics]], a complete set of [[Invariant (mathematics)\|invariant]]s for a [[classification theorems\|classification problem]] is a collection of maps
			:<math>f_i : X \to Y_i \,</math>
			(where ''X'' is the collection of objects being classified, up to some equivalence relation, and the <math>Y_i</math> are some sets), such that <math>x</math> ∼ <math>x'</math> if and only if <math>f_i(x) = f_i(x')</math> for all ''i''. In words, such that two objects are equivalent if and only if all invariants are equal.

			Symbolically, a complete set of invariants is a collection of maps such that
			:<math>\prod f_i : (X/\sim) \to \prod Y_i</math>
			is [[injective]].

			As invariants are, by definition, equal on equivalent objects, equality of invariants is a ''necessary'' condition for equivalence; a ''complete'' set of invariants is a set such that equality of these is ''sufficient'' for equivalence. In the context of a group action, this may be stated as: invariants are functions of [[coinvariant]]s (equivalence classes, orbits), and a complete set of invariants characterizes the coinvariants (is a set of defining equations for the coinvariants).

			==Examples==
			* In the [[classification of two-dimensional closed manifolds]], [[Euler characteristic]] (or [[Genus (mathematics)\|genus]]) and [[orientability]] are a complete set of invariants.
			* [[Jordan normal form]] of a matrix is a complete invariant for matrices up to conjugation, but [[eigenvalue]]s (with multiplicities) are not.

			==Realizability of invariants==
			A complete set of invariants does not immediately yield a [[classification theorem]]: not all combinations of invariants may be realized. Symbolically, one must also determine the image of
			:<math>\prod f_i : X \to \prod Y_i.</math>

			{{DEFAULTSORT:Complete Set Of Invariants}}
			[[Category:Mathematical terminology]]

en>Kiefer.Wolfowitz: Reverted to revision 483338354 by Kiefer.Wolfowitz: Propose draft on talk page. You need help with English spelling, etc. Good ideas, but first talk page draft, then consensus, then article, please. . (TW)

2012-03-26T08:45:25Z

Reverted to revision 483338354 by Kiefer.Wolfowitz: Propose draft on talk page. You need help with English spelling, etc. Good ideas, but first talk page draft, then consensus, then article, please. . (TW)

New page

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