141.20.50.28: /* Definition */

2014-01-29T12:50:00Z

Definition

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	The ~~writer~~ is ~~known by~~ the ~~name of~~ [~~http~~://~~www.newhealthguide.org~~/~~Types-Of-Bacteria.html Figures Wunder~~]. ~~He utilized~~ to be ~~unemployed but now he is a computer operator but his promotion by no means comes~~. ~~South Dakota~~ is ~~exactly where me~~ and ~~my husband reside and my family members loves~~ it. ~~What I adore performing is to [http:~~//~~Stdfreeclinics~~.~~com/SYPHILIS~~.~~html collect badges~~] ~~but I've been [http:~~//~~torontocartridge~~.~~com/uncategorized/~~the-~~ideal-way-~~to-~~battle-~~a~~-yeast-infection/~~ at ~~home std testing~~] ~~home [https://mostlymusiccom~~.~~zendesk~~.~~com/entries/53427870~~-~~Prevent~~-~~Candida~~-~~Albicans-Before-Hand-With-These-Tips std testing at home~~] ~~test using on new issues home std test lately.<br><br>My weblog ..~~. [http://www.~~articlestunner~~.~~com~~/~~cures~~-~~for~~-~~the-yeast-infection-suggestions-to-use-now/~~ http://~~www~~.~~articlestunner~~.~~com/cures-for-the-yeast-infection-suggestions-to-use-now~~/]		{{for \|constraints in Hamiltonian mechanics\|constraint (classical mechanics)\|first class constraint\|primary constraint\|holonomic constraint}}
			In [[mathematics]], a '''constraint''' is a condition of an [[optimization (mathematics)\|optimization]] problem that the solution must satisfy. There are several types of constraints—primarily [[Equality (mathematics)\|equality]] constraints, [[Inequality (mathematics)\|inequality]] constraints, and [[Integer programming\|integer constraints]]. The set of [[candidate solution]]s that satisfy all constraints is called the [[feasible set]].

			==Example==
			The following is a simple optimization problem:

			:<math>\min f(\bold x) = x_1^2+x_2^4 </math>

			subject to

			:<math> x_1 \ge 1 </math>

			and

			:<math> x_2 = 1, \, </math>

			where <math>\bold x</math> denotes the [[Vectorization (mathematics)\|vector]] (''x''<sub>1</sub>, ''x''<sub>2</sub>).

			In this example, the first line defines the function to be minimized (called the ''objective function'', ''[[loss function]]'', or ''cost function''). The second and third lines define two constraints, the first of which is an inequality constraint and the second of which is an equality constraint. These two constraints are hard constraints, meaning that it is required that they be satisfied; they define the feasible set of candidate solutions.

			Without the constraints, the solution would be <math>(0,0)\,</math> where <math>f(\bold x)</math> has the lowest value. But this solution does not satisfy the constraints. The solution of the [[constrained optimization]] problem stated above is <math> \bold x = (1,1)</math>, which is the point with the smallest value of <math>f(\bold x)</math> that satisfies the two constraints.

			== Terminology ==
			* If an inequality constraint holds with ''equality'' at the optimal point, the constraint is said to be '''{{visible anchor\|binding}}''', as the point ''cannot'' be varied in the direction of the constraint even though doing so would improve the value of the objective function.
			* If an inequality constraint holds as a ''strict inequality'' at the optimal point (that is, does not hold with equality), the constraint is said to be '''{{visible anchor\|non-binding}}''', as the point ''could'' be varied in the direction of the constraint, although it would not be optimal to do so. If a constraint is non-binding, the optimization problem would have the same solution even in the absence of that constraint.
			* If a constraint is not satisfied at a given point, the point is said to be '''[[Feasible region\|infeasible]]'''.

			==Hard and soft constraints==

			If the problem mandates that the constraints be satisfied, as in the above discussion, the constraints are sometimes referred to as ''hard constraints''. However, in some problems, called [[Constraint satisfaction problem#Flexible CSPs\|flexible constraint satisfaction problems]], it is preferred but not required that certain constraints be satisfied; such non-mandatory constraints are known as ''[[Constraint optimization#Definition\|soft constraints]]''. Soft constraints arise in, for example, [[preference-based planning]]. In a [[MAX-CSP]] problem, a number of constraints are allowed to be violated, and the quality of a solution is measured by the number of satisfied constraints.

			== See also ==
			* [[Constraint satisfaction problem]]
			* [[Karush–Kuhn–Tucker conditions]]
			* [[Lagrange multipliers]]
			* [[Level set]]
			* [[Linear programming]]
			* [[Nonlinear programming]]

			== External links ==
			*[http://www.neos-guide.org/non-lp-faq Nonlinear programming FAQ]
			*[http://glossary.computing.society.informs.org/ Mathematical Programming Glossary]

			[[Category:Mathematical optimization]]

			[[ca:Restricció]]
			[[es:Restricción (matemáticas)]]

en>Yobot: WP:CHECKWIKI error 61 fixes + general fixes using AWB (8032)

2012-03-21T00:04:17Z

WP:CHECKWIKI error 61 fixes + general fixes using AWB (8032)

New page

The writer is known by the name of [http://www.newhealthguide.org/Types-Of-Bacteria.html Figures Wunder]. He utilized to be unemployed but now he is a computer operator but his promotion by no means comes. South Dakota is exactly where me and my husband reside and my family members loves it. What I adore performing is to [http://Stdfreeclinics.com/SYPHILIS.html collect badges] but I've been [http://torontocartridge.com/uncategorized/the-ideal-way-to-battle-a-yeast-infection/ at home std testing] home [https://mostlymusiccom.zendesk.com/entries/53427870-Prevent-Candida-Albicans-Before-Hand-With-These-Tips std testing at home] test using on new issues home std test lately.<br><br>My weblog ... [http://www.articlestunner.com/cures-for-the-yeast-infection-suggestions-to-use-now/ http://www.articlestunner.com/cures-for-the-yeast-infection-suggestions-to-use-now/]

Aitken's delta-squared process - Revision history

141.20.50.28: /* Definition */

en>Yobot: WP:CHECKWIKI error 61 fixes + general fixes using AWB (8032)