QPALM
1.2.0
Proximal Augmented Lagrangian method for Quadratic Programs
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QPALM
include
qpalm
scaling.h
Go to the documentation of this file.
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/**
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* @file scaling.h
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* @author Ben Hermans
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* @brief Problem data scaling during setup.
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* @details This file includes the routine that is called during setup to scale the problem data,
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* and initial guesses if the problem is warm-started. Scaling the problem is useful to prevent
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* large changes in the active set and to guard against ill-conditioning in the objective function.
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*
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*/
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#ifndef SCALING_H
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# define SCALING_H
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# ifdef __cplusplus
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extern
"C"
{
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# endif
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// Functions to scale problem data
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# include "
types.h
"
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# include "
lin_alg.h
"
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# include "
constants.h
"
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/**
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* Scale problem matrices
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*
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* Ruiz scaling \cite ruiz2001scaling is applied to the constraint matrix A. This means that the rows and columns of A are
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* scaled elementwise by the square root of their infinity norm, and this for a number of work->settings->scaling
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* iterations. The resulting scaling can be written as @f$\bar{A}\leftarrow EAD@f$, where @f$E@f$ and
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* @f$D@f$ are the row and column scaling diagonal matrices respectively. The upper and lower bounds
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* are also scaled with @f$E@f$, thus @f$\bar{b}_\textrm{min}, \bar{b}_\textrm{max} \leftarrow
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* E b_\textrm{min}, E b_\textrm{max}@f$. The primal variables are transformed using @f$D^{-1}@f$,
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* resulting in @f$\bar{x}\leftarrow D^{-1}x@f$. Therefore, also the cost matrix Q and vector q have
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* to be scaled with @f$D@f$, @f$\bar{Q}\leftarrow DQD@f$ and @f$\bar{q}\leftarrow Dq@f$. Finally the
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* objective function is scaled with a scalar @f$c@f$, thus @f$\bar{Q}, \bar{q} \leftarrow c\bar{Q},
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* c\bar{q} @f$, where @f$c=1/\textrm{max}(1, \nabla f(x_0))@f$. The dual variables in the scaled problem
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* become @f$\bar{y} \leftarrow c E^{-1} y@f$. The diagonals of @f$D@f$ and @f$E@f$ are stored and used in the
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* remainder of the problem.
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*
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*
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*
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* @param work Workspace
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*/
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void
scale_data
(
QPALMWorkspace
*work);
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/**
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* Unscale the problem data. See scale_data.
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*
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* @param work Workspace
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*/
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void
unscale_data
(
QPALMWorkspace
*work);
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# ifdef __cplusplus
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}
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# endif
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#endif
// ifndef SCALING_H
constants.h
Constants used in QPALM.
lin_alg.h
Linear algebra with vectors.
scale_data
void scale_data(QPALMWorkspace *work)
Scale problem matrices.
Definition
scaling.c:31
unscale_data
void unscale_data(QPALMWorkspace *work)
Unscale the problem data.
Definition
scaling.c:99
QPALMWorkspace
QPALM Workspace.
Definition
types.h:197
types.h
Internal data structures used in QPALM.
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