idol::Tolerance Namespace Reference

Variables
static double	Sparsity = 1e-8
static unsigned int	Digits = 8
static double	MIPRelativeGap = 1e-4
static double	MIPAbsoluteGap = 1e-5
static double	Integer = 10e-5
static double	Feasibility = 10e-6
static double	Optimality = 10e-6

Detailed Description

Stores the default high-level tolerances used in idol.

It is possible for external-mip to have additional tolerance parameters, yet, the tolerances defined in this namespace should always be taken into account by the optimizer. Apart from the Sparsity tolerance, users can also change tolerance values at a local level (i.e., at an optimizer level) rather than at a global level.

Variable Documentation

Digits

unsigned int idol::Tolerance::Digits = 8

static

Definition at line 39 of file numericals.h.

Feasibility

double idol::Tolerance::Feasibility = 10e-6

static

Default: \( 10^{-6} \)

Recommended range: \( [ 10^{-9}, 10^{-2} ] \)

Used to characterized constraint satisfaction, i.e., a constraint is satisfied if it is not violated by a larger amount than this tolerance.

Definition at line 83 of file numericals.h.

Integer

double idol::Tolerance::Integer = 10e-5

static

Default: \( 10^{-5} \)

Recommended range: \( [ 10^{-9}, 10^{-1} ] \)

Used to recognized integer values, i.e., a given value is considered integer when the closest integer point is closer than this tolerance.

Definition at line 73 of file numericals.h.

MIPAbsoluteGap

double idol::Tolerance::MIPAbsoluteGap = 1e-5

static

Default: \( 10^{-5} \)

Recommended range: \( [ 0, \infty ] \)

Used to declare optimality of a MIP solution by comparing with the current absolute gap.

The absolute gap is computed as follows:

\[ \gamma_{\text{abs}} := |UB - LB| \]

Definition at line 63 of file numericals.h.

MIPRelativeGap

double idol::Tolerance::MIPRelativeGap = 1e-4

static

Default: \( 10^{-4} \)

Recommended range: \( [ 0, +\infty ] \)

Used to declare optimality of a MIP solution by comparing with the current relative gap.

The relative gap is computed as follows:

\[ \gamma_{\text{rel}} := \frac{ |UB - LB| }{ 10^{-10} + |UB| }. \]

Definition at line 51 of file numericals.h.

Optimality

double idol::Tolerance::Optimality = 10e-6

static

Default: \( 10^{-6} \)

Recommended range: \( [ 10^{-9}, 10^{-2} ] \)

Used to characterize optimality, i.e., all reduced costs must be smaller than this tolerance.

Definition at line 92 of file numericals.h.

Sparsity

double idol::Tolerance::Sparsity = 1e-8

static

Default: \( 10^{-8} \)

Recommended range: \( [ 10^{-10}, 10^{-5} ] \)

This tolerance is used when data is saved in a sparse manner. For instance, when a value close to zero should be stored or ignored when saving a primal point.

Definition at line 37 of file numericals.h.