CpTransf - Revision history

Elias at 12:16, 10 January 2012

2012-01-10T12:16:00Z

← Older revision		Revision as of 07:16, 10 January 2012
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	==Calling Syntax==		==Calling Syntax==

	<~~syntaxhighlight~~ lang="matlab">		<source lang="matlab">
	[AA, bb, meq] = cpTransf(Prob, TransfType, makeEQ, LowInf)		[AA, bb, meq] = cpTransf(Prob, TransfType, makeEQ, LowInf)
	</~~syntaxhighlight~~>		</source>

	==Inputs==		==Inputs==
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	values):		values):

	<~~syntaxhighlight~~ lang="matlab">		<source lang="matlab">
	x(~x_L==x_U) = (x-x_L) + x_L(~x_L==x_U)		x(~x_L==x_U) = (x-x_L) + x_L(~x_L==x_U)
	</~~syntaxhighlight~~>		</source>

	If ''TransType ''= 2 the program is transformed into the form		If ''TransType ''= 2 the program is transformed into the form

Elias at 14:55, 8 December 2011

2011-12-08T14:55:50Z

← Older revision		Revision as of 09:55, 8 December 2011
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	where <math>x,x_{L},x_{U}\in \~~MATHSET~~{R}^{n}</math>, <math>A\in \~~MATHSET~~{R}^{m\times n}</math>		where <math>x,x_{L},x_{U}\in \mathbb{R}^{n}</math>, <math>A\in \mathbb{R}^{m\times n}</math>
	and <math>b_{L},b_{U} \in \~~MATHSET~~{R}^{m}</math>, to other forms.		and <math>b_{L},b_{U} \in \mathbb{R}^{m}</math>, to other forms.

	==Calling Syntax==		==Calling Syntax==

Elias at 14:54, 22 July 2011

2011-07-22T14:54:42Z

← Older revision		Revision as of 09:54, 22 July 2011
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			[[Category:Utility Functions]]
	==Purpose==		==Purpose==

Elias: /* Description */

2011-07-22T11:57:40Z

Description

← Older revision		Revision as of 06:57, 22 July 2011
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	where the first ''meq ''constraints are equalities.		where the first ''meq ''constraints are equalities.



	If ''TransType'' = 3 the program is transformed into the form		If ''TransType'' = 3 the program is transformed into the form

Elias: /* Inputs */

2011-07-22T11:56:44Z

Inputs

← Older revision		Revision as of 06:56, 22 July 2011
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	\|''LowInf ''\|\|Variables equal to ''-Inf'' or variables ''< LowInf ''are set to ''LowInf ''before transforming		\|''LowInf ''\|\|Variables equal to ''-Inf'' or variables ''< LowInf ''are set to ''LowInf ''before transforming

	the problem. Default ''-''10''-''4 . ''<nowiki>\|</nowiki>~~LowI nf~~ <nowiki>\|</nowiki> ''are limit if upper bound variables are to be used.		the problem. Default ''-''10''-''4 . ''<nowiki>\|</nowiki>LowInf<nowiki>\|</nowiki> ''are limit if upper bound variables are to be used.
	\|}		\|}

Elias: Created page with "==Purpose== Transform general convex programs on the form $\begin{array}{cccccl} \min\limits_{x} & f(x) & & & & \\s/t & x_{L} & \leq & x & \leq & x_{U} \\& b_{L} ..."$

2011-07-22T11:55:33Z

Created page with "==Purpose== Transform general convex programs on the form <math> \begin{array}{cccccl} \min\limits_{x} & f(x) & & & & \\s/t & x_{L} & \leq & x & \leq & x_{U} \\& b_{L} ..."

New page

==Purpose==

Transform general convex programs on the form

<math>
\begin{array}{cccccl}
\min\limits_{x} & f(x) & & & & \\s/t & x_{L} & \leq & x & \leq & x_{U} \\& b_{L} & \leq & Ax & \leq &

b_{U}\\
\end{array}
</math>

where <math>x,x_{L},x_{U}\in \MATHSET{R}^{n}</math>, <math>A\in \MATHSET{R}^{m\times n}</math>
and <math>b_{L},b_{U} \in \MATHSET{R}^{m}</math>, to other forms.

==Calling Syntax==

<syntaxhighlight lang="matlab">
[AA, bb, meq] = cpTransf(Prob, TransfType, makeEQ, LowInf)
</syntaxhighlight>

==Inputs==

{| class="wikitable"
!Input||Description
|-valign="top"
|''Prob''||Problem description structure. The following fields are used:

''QP.c'' Constant vector ''c ''in ''c<sup>T</sup>x''.

''A'' Constraint matrix for linear constraints.

''b_L'' Lower bounds on the linear constraints.

''b U'' Upper bounds on the linear constraints.

''x_L'' Lower bounds on the variables.

''x_U'' Upper bounds on the variables.
|-valign="top"
|''TransfType''||Type of transformation, see the description below.
|-valign="top"
|''MakeEQ''||Flag, if set true, make standard form (all equalities).
|-valign="top"
|''LowInf ''||Variables equal to ''-Inf'' or variables ''< LowInf ''are set to ''LowInf ''before transforming

the problem. Default ''-''10''-''4 . ''<nowiki>|</nowiki>LowI nf <nowiki>|</nowiki> ''are limit if upper bound variables are to be used.
|}

==Outputs==

{| class="wikitable"
!Output||Description
|-
|''AA''||The expanded linear constraint matrix.
|-
|''bb''||The expanded upper bounds for the linear constraints.
|-
|''meq''||The first ''meq ''equations are equalities.
|}

==Description==

If ''TransType ''= 1 the program is transformed into the form

<math>
\begin{array}{cccc}
\min\limits_{x} & f(x-x_L) & & \\s/t & AA(x-x_L) & \leq & bb \\& x-x_L & \geq & 0 \\
\end{array}
</math>

where the first ''meq ''constraints are equalities. Translate back with (fixed variables do not change their

values):

<syntaxhighlight lang="matlab">
x(~x_L==x_U) = (x-x_L) + x_L(~x_L==x_U)
</syntaxhighlight>

If ''TransType ''= 2 the program is transformed into the form

<math>
\begin{array}{cccccl}
\min\limits_{x} & f(x) & & \\s/t & & & AA(x) & \leq & bb \\& x_{L} & \leq & x & \leq

& x_{U} \\
\end{array}
</math>

where the first ''meq ''constraints are equalities.

If ''TransType'' = 3 the program is transformed into the form

<math>
\begin{array}{cccc}
\min\limits_{x} & f(x) & & \\s/t & AA x & \leq & bb \\ & x & \geq & x_L \\\end{array}
</math>

where the first ''meq''constraints are equalities.