QPALM main
Proximal Augmented Lagrangian method for Quadratic Programs
Loading...
Searching...
No Matches
Functions
scaling.h File Reference

Detailed Description

Problem data scaling during setup.

Author
Ben Hermans

This file includes the routine that is called during setup to scale the problem data, and initial guesses if the problem is warm-started. Scaling the problem is useful to prevent large changes in the active set and to guard against ill-conditioning in the objective function.

Definition in file scaling.h.

#include "types.h"
#include "lin_alg.h"
#include "constants.h"
+ Include dependency graph for scaling.h:
+ This graph shows which files directly or indirectly include this file:

Go to the source code of this file.

Functions

void scale_data (QPALMWorkspace *work)
 Scale problem matrices.
 
void unscale_data (QPALMWorkspace *work)
 Unscale the problem data.
 

Function Documentation

◆ scale_data()

void scale_data ( QPALMWorkspace work)

Scale problem matrices.

Ruiz scaling [4] is applied to the constraint matrix A. This means that the rows and columns of A are scaled elementwise by the square root of their infinity norm, and this for a number of work->settings->scaling iterations. The resulting scaling can be written as \(\bar{A}\leftarrow EAD\), where \(E\) and \(D\) are the row and column scaling diagonal matrices respectively. The upper and lower bounds are also scaled with \(E\), thus \(\bar{b}_\textrm{min}, \bar{b}_\textrm{max} \leftarrow E b_\textrm{min}, E b_\textrm{max}\). The primal variables are transformed using \(D^{-1}\), resulting in \(\bar{x}\leftarrow D^{-1}x\). Therefore, also the cost matrix Q and vector q have to be scaled with \(D\), \(\bar{Q}\leftarrow DQD\) and \(\bar{q}\leftarrow Dq\). Finally the objective function is scaled with a scalar \(c\), thus \(\bar{Q}, \bar{q} \leftarrow c\bar{Q}, c\bar{q} \), where \(c=1/\textrm{max}(1, \nabla f(x_0))\). The dual variables in the scaled problem become \(\bar{y} \leftarrow c E^{-1} y\). The diagonals of \(D\) and \(E\) are stored and used in the remainder of the problem.

Parameters
workWorkspace

Definition at line 31 of file scaling.c.

+ Here is the call graph for this function:

◆ unscale_data()

void unscale_data ( QPALMWorkspace work)

Unscale the problem data.

See scale_data.

Parameters
workWorkspace

Definition at line 99 of file scaling.c.

+ Here is the call graph for this function: