Numerical Analysis

Analyzer() <: MathOptAnalyzer.AbstractAnalyzer

The Analyzer type is used to analyze the coefficients of a model for numerical issues.

Example

julia> data = MathOptAnalyzer.analyze(
    MathOptAnalyzer.Numerical.Analyzer(),
    model;
    threshold_dense_fill_in = 0.10,
    threshold_dense_entries = 1000,
    threshold_small = 1e-5,
    threshold_large = 1e+5,
    threshold_dynamic_range_single = 1e+6,
    threshold_dynamic_range_matrix = 1e+8,
)

The additional parameters:

• threshold_dense_fill_in: The threshold for the fraction of non-zero entries in a constraint to be considered dense.
• threshold_dense_entries: The minimum number of non-zero entries for a constraint to be considered dense.
• threshold_small: The threshold for small coefficients in the model.
• threshold_large: The threshold for large coefficients in the model.
• threshold_dynamic_range_single: The threshold for the range of coefficients in the model with respect with individual columns, rows, objective coefficients and rhs coefficients.
• threshold_dynamic_range_matrix: The threshold for the range of coefficients in the model with respect to the matrix of coefficients.

AbstractNumericalIssue <: AbstractNumericalIssue

Abstract type for numerical issues found during the analysis of a model.

VariableNotInConstraints <: AbstractNumericalIssue

The VariableNotInConstraints issue is identified when a variable appears in no constraints.

For more information, run:

julia> MathOptAnalyzer.summarize(MathOptAnalyzer.Numerical.VariableNotInConstraints)

EmptyConstraint <: AbstractNumericalIssue

The EmptyConstraint issue is identified when a constraint has no coefficients different from zero.

For more information, run:

julia> MathOptAnalyzer.summarize(MathOptAnalyzer.Numerical.EmptyConstraint)

VariableBoundAsConstraint <: AbstractNumericalIssue

The VariableBoundAsConstraint issue is identified when a constraint is equivalent to a variable bound, that is, the constraint has only one non-zero coefficient, and this coefficient is equal to one.

For more information, run:

julia> MathOptAnalyzer.summarize(MathOptAnalyzer.Numerical.VariableBoundAsConstraint)

DenseConstraint <: AbstractNumericalIssue

The DenseConstraint issue is identified when a constraint has a fraction of non-zero entries greater than threshold_dense_fill_in and the number of non-zero entries is greater than threshold_dense_entries.

For more information, run:

julia> MathOptAnalyzer.summarize(MathOptAnalyzer.Numerical.DenseConstraint)

SmallMatrixCoefficient <: AbstractNumericalIssue

The SmallMatrixCoefficient issue is identified when a matrix coefficient in a constraint is smaller than threshold_small.

For more information, run:

julia> MathOptAnalyzer.summarize(MathOptAnalyzer.Numerical.SmallMatrixCoefficient)

LargeMatrixCoefficient <: AbstractNumericalIssue

The LargeMatrixCoefficient issue is identified when a matrix coefficient in a constraint is larger than threshold_large.

For more information, run:

julia> MathOptAnalyzer.summarize(MathOptAnalyzer.Numerical.LargeMatrixCoefficient)

SmallBoundCoefficient <: AbstractNumericalIssue

The SmallBoundCoefficient issue is identified when a variable's bound (coefficient) is smaller than threshold_small.

For more information, run:

julia> MathOptAnalyzer.summarize(MathOptAnalyzer.Numerical.SmallBoundCoefficient)

LargeBoundCoefficient <: AbstractNumericalIssue

The LargeBoundCoefficient issue is identified when a variable's bound (coefficient) is larger than threshold_large.

For more information, run:

julia> MathOptAnalyzer.summarize(MathOptAnalyzer.Numerical.LargeBoundCoefficient)

SmallRHSCoefficient <: AbstractNumericalIssue

The SmallRHSCoefficient issue is identified when the right-hand-side (RHS) coefficient of a constraint is smaller than threshold_small.

For more information, run:

julia> MathOptAnalyzer.summarize(MathOptAnalyzer.Numerical.SmallRHSCoefficient)

LargeRHSCoefficient <: AbstractNumericalIssue

The LargeRHSCoefficient issue is identified when the right-hand-side (RHS) coefficient of a constraint is larger than threshold_large.

For more information, run:

julia> MathOptAnalyzer.summarize(MathOptAnalyzer.Numerical.LargeRHSCoefficient)

SmallObjectiveCoefficient <: AbstractNumericalIssue

The SmallObjectiveCoefficient issue is identified when a coefficient in the objective function is smaller than threshold_small.

For more information, run:

julia> MathOptAnalyzer.summarize(MathOptAnalyzer.Numerical.SmallObjectiveCoefficient)

LargeObjectiveCoefficient <: AbstractNumericalIssue

The LargeObjectiveCoefficient issue is identified when a coefficient in the objective function is larger than threshold_large.

For more information, run:

julia> MathOptAnalyzer.summarize(MathOptAnalyzer.Numerical.LargeObjectiveCoefficient)

SmallObjectiveQuadraticCoefficient <: AbstractNumericalIssue

The SmallObjectiveQuadraticCoefficient issue is identified when a quadratic coefficient in the objective function is smaller than threshold_small.

For more information, run:

julia> MathOptAnalyzer.summarize(
    MathOptAnalyzer.Numerical.SmallObjectiveQuadraticCoefficient
)

LargeObjectiveQuadraticCoefficient <: AbstractNumericalIssue

The LargeObjectiveQuadraticCoefficient issue is identified when a quadratic coefficient in the objective function is larger than threshold_large.

For more information, run:

julia> MathOptAnalyzer.summarize(
    MathOptAnalyzer.Numerical.LargeObjectiveQuadraticCoefficient
)

SmallMatrixQuadraticCoefficient <: AbstractNumericalIssue

The SmallMatrixQuadraticCoefficient issue is identified when a quadratic coefficient in a constraint is smaller than threshold_small.

For more information, run:

julia> MathOptAnalyzer.summarize(
    MathOptAnalyzer.Numerical.SmallMatrixQuadraticCoefficient
)

LargeMatrixQuadraticCoefficient <: AbstractNumericalIssue

The LargeMatrixQuadraticCoefficient issue is identified when a quadratic coefficient in a constraint is larger than threshold_large.

For more information, run:

julia> MathOptAnalyzer.summarize(
    MathOptAnalyzer.Numerical.LargeMatrixQuadraticCoefficient
)

NonconvexQuadraticObjective <: AbstractNumericalIssue

The NonconvexQuadraticObjective issue is identified when a quadratic objective function is non-convex.

For more information, run:

julia> MathOptAnalyzer.summarize(
    MathOptAnalyzer.Numerical.NonconvexQuadraticObjective
)

NonconvexQuadraticConstraint

The NonconvexQuadraticConstraint issue is identified when a quadratic constraint is non-convex.

For more information, run:

julia> MathOptAnalyzer.summarize(
    MathOptAnalyzer.Numerical.NonconvexQuadraticConstraint
)

LargeDynamicRangeConstraint <: AbstractNumericalIssue

The LargeDynamicRangeConstraint issue is identified when the dynamic range of a constraint is larger than threshold_dynamic_range_single. The dynamic range is defined as the ratio between the largest and smallest coefficients of the constraint.

For more information, run:

julia> MathOptAnalyzer.summarize(
    MathOptAnalyzer.Numerical.LargeDynamicRangeConstraint
)

LargeDynamicRangeMatrix <: AbstractNumericalIssue

The LargeDynamicRangeMatrix issue is identified when the dynamic range of the matrix is larger than threshold_dynamic_range_matrix. The dynamic range is defined as the ratio between the largest and smallest coefficients of the matrix.

For more information, run:

julia> MathOptAnalyzer.summarize(
    MathOptAnalyzer.Numerical.LargeDynamicRangeMatrix
)

LargeDynamicRangeObjective <: AbstractNumericalIssue

The LargeDynamicRangeObjective issue is identified when the dynamic range of the objective function is larger than threshold_dynamic_range_single. The dynamic range is defined as the ratio between the largest and smallest coefficients of the objective function.

For more information, run:

julia> MathOptAnalyzer.summarize(
    MathOptAnalyzer.Numerical.LargeDynamicRangeObjective
)

LargeDynamicRangeRHS <: AbstractNumericalIssue

The LargeDynamicRangeRHS issue is identified when the dynamic range of the right-hand side (RHS) vector is larger than threshold_dynamic_range_rhs. The dynamic range is defined as the ratio between the largest and smallest coefficients of the RHS vector.

For more information, run:

julia> MathOptAnalyzer.summarize(
    MathOptAnalyzer.Numerical.LargeDynamicRangeRHS
)

LargeDynamicRangeVariable <: AbstractNumericalIssue

The LargeDynamicRangeVariable issue is identified when the dynamic range of a variable is larger than threshold_dynamic_range_single. The dynamic range is defined as the ratio between the largest and smallest coefficients of the variable inall constraint it appears.

For more information, run:

julia> MathOptAnalyzer.summarize(
    MathOptAnalyzer.Numerical.LargeDynamicRangeVariable
)

LargeDynamicRangeBound <: AbstractNumericalIssue

The LargeDynamicRangeBound issue is identified when the dynamic range of the variables bounds is larger than threshold_dynamic_range_single. The dynamic range is defined as the ratio between the largest and smallest bounds of all variables. For more information, run:

julia> MathOptAnalyzer.summarize(
    MathOptAnalyzer.Numerical.LargeDynamicRangeBound
)

Data

The Data structure holds the results of the analysis performed by the MathOptAnalyzer.Numerical.Analyzer. It contains various thresholds and the information about the model's variables, constraints, and objective function.