Problem data scaling during setup. More...

#include "types.h"
#include "lin_alg.h"
#include "constants.h"

Functions
void	scale_data (QPALMWorkspace *work)
	Scale problem matrices. More...

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.

Note: The function in this file makes use of the cholmod scale routines.

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.

Note: This function makes use of the cholmod scale routines.

Parameters

work Workspace

Functions

Detailed Description

Function Documentation

◆ scale_data()