Legendrian knot - Revision history

en>Rjwilmsi: /* References */Added 2 dois to journal cites using AWB (10210)

2014-05-24T10:14:30Z

References: Added 2 dois to journal cites using AWB (10210)

← Older revision		Revision as of 12:14, 24 May 2014
Line 1:		Line 1:
	~~{{Context\|date=October 2009}}~~		over the counter std test ([http://www.hotporn123.com/user/RPocock official statement]) writer is called Irwin. Puerto Rico is exactly where he's always been living but she requirements to move because of her family. Playing baseball is the pastime he will by no means quit performing. I am a meter reader.
	~~{{Unreferenced\|date=October 2006}}~~
	~~'''Sequential quadratic programming'''~~ (~~'''SQP''') is an~~ [[iterative method]] for [[nonlinear programming\|nonlinear optimization]]. SQP methods are used on problems for which the [[objective function]] and the constraints are twice [[continuously differentiable]].

	SQP methods solve a sequence of optimization subproblems, each of which optimizes a quadratic model of the objective subject to a linearization of the constraints. If the problem is unconstrained, then the method reduces to [[Newton's method]] for finding a point where the gradient of the objective vanishes. If the problem has only equality constraints, then the method is equivalent to applying [[Newton's method]] to the first-order optimality conditions, or [[Karush–Kuhn–Tucker conditions]], of the problem. SQP methods have been implemented in many packages, including [[NPSOL]], [[SNOPT]], [[NLPQL]], [[OPSYC]], [[OPTIMA]], [[MATLAB]] and SQP.

	~~==Algorithm basics==~~
	~~Consider a [[nonlinear programming]] problem of the form:~~

	~~:<math>\begin{array}{rl}~~
	~~\min\limits_{x} & f(x) \\~~
	~~\mbox{s.t.} & b(x) \ge 0 \\~~
	~~& c(x) = 0.~~
	~~\end{array}</math>~~

	~~The Lagrangian for this problem is;~~
	:~~<math>\mathcal{L}(x,\lambda,\sigma) = f(x) - \lambda^T b(x) - \sigma^T c(x),<~~/~~math>~~

	~~where <math>\lambda<~~/~~math> and <math>\sigma</math> are [[Lagrange multipliers]]~~. ~~At an iterate <math>x_k<~~/~~math>, a basic sequential quadratic programming algorithm defines an appropriate search direction <math>d_k<~~/~~math> as a solution to the [[quadratic programming~~]~~] subproblem~~

	~~:<math>\begin{array}{rl} \min\limits_{d} & f(x_k~~) ~~+ \nabla f(x_k)^Td + \tfrac{1}{2} d^T \nabla_{xx}^2 \mathcal{L}(x_k,\lambda_k,\sigma_k) d \\~~
	~~\mathrm{s.t.} & b(x_k) + \nabla b(x_k)^Td \ge 0 \\~~
	~~& c(x_k) + \nabla c(x_k)^T d = 0~~. ~~\end{array}</math>~~

	~~Note that the term <math>f(x_k)</math> in the expression above may be left out for the minimization problem, since it~~ is ~~constant.~~

	~~==See also==~~
	* [[Sequential linear programming]]
	* [[Secant method]]
	* [[Newton's ~~method]]~~

	~~==References==~~
	* {{cite book\|last1=Bonnans\|first1=J. Frédéric\|last2=Gilbert\|first2=J. Charles\|last3=Lemaréchal\|first3=Claude\|last4=Sagastizábal\|first4=Claudia A.\|title=Numerical optimization: Theoretical and practical aspects\|url=http://www.springer.com/mathematics/applications/book/978-3-540-35445-1\|edition=Second revised ed. of translation of 1997 <!-- ''Optimisation numérique: Aspects théoriques et pratiques'' --> French\| series=Universitext\|publisher=Springer-Verlag\|location=Berlin\|year=2006\|pages=xiv+490\|isbn=3-540-35445-X\|doi=10.~~1007/978-3-540-35447-5\|mr=2265882\|unused_data=<!-- authorlink3=Claude Lemaréchal -->}}~~
	* {{ cite book \| year=2006\|url=http://www.~~ece.northwestern.edu/~nocedal/book/num-opt.html\| title= Numerical Optimization\| publisher=Springer.\|isbn=0-387-30303-0\| author=Jorge Nocedal and Stephen J~~. ~~Wright}}~~

	~~==External links==~~
	* [http://www.neos-guide.org/content/sequential-quadratic-programming Sequential Quadratic Programming at NEOS guide]

	~~{{optimization algorithms}}~~

	~~[[Category:Optimization algorithms and methods]]~~


	~~{{Mathapplied-stub}}~~

en>David Eppstein: remove stale and unexplained expert tag — the talk page refers to a request for inline citations but this seems to have been already resolved

2014-01-21T22:02:22Z

remove stale and unexplained expert tag — the talk page refers to a request for inline citations but this seems to have been already resolved

← Older revision		Revision as of 00:02, 22 January 2014
Line 1:		Line 1:
	~~Nice~~ to ~~meet you~~, ~~my title~~ is ~~Figures Held although I don~~'t ~~really like becoming called like that~~. ~~She~~ is a ~~librarian but she'~~s ~~always needed her own business~~. ~~California~~ is ~~exactly where her~~ [http://www.~~blaze16~~.com/~~blog~~/~~257588 std testing at home] is but she needs to transfer because~~ of ~~her family~~. ~~What I adore doing is taking part in baseball but I haven't made a dime with it~~.		{{Context\|date=October 2009}}
			{{Unreferenced\|date=October 2006}}
			'''Sequential quadratic programming''' ('''SQP''') is an [[iterative method]] for [[nonlinear programming\|nonlinear optimization]]. SQP methods are used on problems for which the [[objective function]] and the constraints are twice [[continuously differentiable]].

			SQP methods solve a sequence of optimization subproblems, each of which optimizes a quadratic model of the objective subject to a linearization of the constraints. If the problem is unconstrained, then the method reduces to [[Newton's method]] for finding a point where the gradient of the objective vanishes. If the problem has only equality constraints, then the method is equivalent to applying [[Newton's method]] to the first-order optimality conditions, or [[Karush–Kuhn–Tucker conditions]], of the problem. SQP methods have been implemented in many packages, including [[NPSOL]], [[SNOPT]], [[NLPQL]], [[OPSYC]], [[OPTIMA]], [[MATLAB]] and SQP.

			==Algorithm basics==
			Consider a [[nonlinear programming]] problem of the form:

			:<math>\begin{array}{rl}
			\min\limits_{x} & f(x) \\
			\mbox{s.t.} & b(x) \ge 0 \\
			& c(x) = 0.
			\end{array}</math>

			The Lagrangian for this problem is;
			:<math>\mathcal{L}(x,\lambda,\sigma) = f(x) - \lambda^T b(x) - \sigma^T c(x),</math>

			where <math>\lambda</math> and <math>\sigma</math> are [[Lagrange multipliers]]. At an iterate <math>x_k</math>, a basic sequential quadratic programming algorithm defines an appropriate search direction <math>d_k</math> as a solution to the [[quadratic programming]] subproblem

			:<math>\begin{array}{rl} \min\limits_{d} & f(x_k) + \nabla f(x_k)^Td + \tfrac{1}{2} d^T \nabla_{xx}^2 \mathcal{L}(x_k,\lambda_k,\sigma_k) d \\
			\mathrm{s.t.} & b(x_k) + \nabla b(x_k)^Td \ge 0 \\
			& c(x_k) + \nabla c(x_k)^T d = 0. \end{array}</math>

			Note that the term <math>f(x_k)</math> in the expression above may be left out for the minimization problem, since it is constant.

			==See also==
			* [[Sequential linear programming]]
			* [[Secant method]]
			* [[Newton's method]]

			==References==
			* {{cite book\|last1=Bonnans\|first1=J. Frédéric\|last2=Gilbert\|first2=J. Charles\|last3=Lemaréchal\|first3=Claude\|last4=Sagastizábal\|first4=Claudia A.\|title=Numerical optimization: Theoretical and practical aspects\|url=http://www.springer.com/mathematics/applications/book/978-3-540-35445-1\|edition=Second revised ed. of translation of 1997 <!-- ''Optimisation numérique: Aspects théoriques et pratiques'' --> French\| series=Universitext\|publisher=Springer-Verlag\|location=Berlin\|year=2006\|pages=xiv+490\|isbn=3-540-35445-X\|doi=10.1007/978-3-540-35447-5\|mr=2265882\|unused_data=<!-- authorlink3=Claude Lemaréchal -->}}
			* {{ cite book \| year=2006\|url=http://www.ece.northwestern.edu/~nocedal/book/num-opt.html\| title= Numerical Optimization\| publisher=Springer.\|isbn=0-387-30303-0\| author=Jorge Nocedal and Stephen J. Wright}}

			==External links==
			* [http://www.neos-guide.org/content/sequential-quadratic-programming Sequential Quadratic Programming at NEOS guide]

			{{optimization algorithms}}

			[[Category:Optimization algorithms and methods]]


			{{Mathapplied-stub}}

en>Helpful Pixie Bot: ISBNs (Build KC)

2012-05-06T00:22:40Z

ISBNs (Build KC)

New page

Nice to meet you, my title is Figures Held although I don't really like becoming called like that. She is a librarian but she's always needed her own business. California is exactly where her [http://www.blaze16.com/blog/257588 std testing at home] is but she needs to transfer because of her family. What I adore doing is taking part in baseball but I haven't made a dime with it.