Lagrange Multipliers: Difference between revisions

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{{CommandManualMenu}}
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This command is used to construct a Penalty constraint handler, which enforces the constraints using the penalty method. The following is the command to construct a plain constraint handler:
This command is used to construct a LagrangeMultiplier constraint handler, which enforces the constraints by introducing Lagrange multiplies to the system of equation. The following is the command to construct a plain constraint handler:




{|  
{|  
| style="background:yellow; color:black; width:800px" | '''constraints Penalty $alphaS $alphaM '''
| style="background:yellow; color:black; width:800px" | '''constraints Lagrange <$alphaS $alphaM >'''
|}
|}


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{|
{|
|  style="width:150px" | '''$alphaS ''' || penalty <math>\alpha_S</math> factor on single point constraints
|  style="width:150px" | '''$alphaS ''' || <math>\alpha_S</math> factor on singe points. optional, default = 1.0
|-
|-
|  '''$alphaM''' || penalty <math>\alpha_M</math> factor on multi-point constraints
|  '''$alphaM''' || <math>\alpha_M</math> factor on multi-points, optional default = 1.0;
 
|}
|}


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NOTES:
NOTES:
* The degree to which the constraints are enforced is dependent on the penalty values chosen. Problems can arise if these values are too small (constraint not enforced strongly enough) or too large (problems associated with conditioning of the system of equations).
* The Lagrange multiplier method introduces new unknowns to the system of equations. The diagonal part of the system corresponding to these new unknowns is 0.0. This ensure that the system IS NOT symmetric positive definite.
 


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Latest revision as of 07:51, 9 June 2016



This command is used to construct a LagrangeMultiplier constraint handler, which enforces the constraints by introducing Lagrange multiplies to the system of equation. The following is the command to construct a plain constraint handler:


constraints Lagrange <$alphaS $alphaM >


$alphaS <math>\alpha_S</math> factor on singe points. optional, default = 1.0
$alphaM <math>\alpha_M</math> factor on multi-points, optional default = 1.0;

NOTES:

  • The Lagrange multiplier method introduces new unknowns to the system of equations. The diagonal part of the system corresponding to these new unknowns is 0.0. This ensure that the system IS NOT symmetric positive definite.

THEORY:


Code Developed by: fmk

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