CpTransf: Difference between revisions
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where <math>x,x_{L},x_{U}\in \ | 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 \ | and <math>b_{L},b_{U} \in \mathbb{R}^{m}</math>, to other forms. | ||
==Calling Syntax== | ==Calling Syntax== |
Revision as of 10:55, 8 December 2011
Purpose
Transform general convex programs on the form
where ,
and , to other forms.
Calling Syntax
[AA, bb, meq] = cpTransf(Prob, TransfType, makeEQ, LowInf)
Inputs
Input | Description |
---|---|
Prob | Problem description structure. The following fields are used:
QP.c Constant vector c in cTx. 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. |
TransfType | Type of transformation, see the description below. |
MakeEQ | Flag, if set true, make standard form (all equalities). |
LowInf | Variables equal to -Inf or variables < LowInf are set to LowInf before transforming
the problem. Default -10-4 . |LowInf| are limit if upper bound variables are to be used. |
Outputs
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
where the first meq constraints are equalities. Translate back with (fixed variables do not change their
values):
x(~x_L==x_U) = (x-x_L) + x_L(~x_L==x_U)
If TransType = 2 the program is transformed into the form
where the first meq constraints are equalities.
If TransType = 3 the program is transformed into the form
where the first meqconstraints are equalities.