properties.md

Test Function Properties

This page documents the properties used to classify benchmark functions in NonlinearOptimizationTestFunctions.jl. Properties are string tags stored in a Set{String} and describe mathematical characteristics of each function. They are rigorously validated against a fixed list to ensure consistency.

Current Statistics (as of December 2025)

The package currently contains 205 benchmark functions.

Property distribution:

Count	Property	Percentage
196	continuous	95.6%
173	differentiable	84.4%
155	bounded	75.6%
147	multimodal	71.7%
141	non-separable	68.8%
73	scalable	35.6%
71	non-convex	34.6%
55	separable	26.8%
55	unimodal	26.8%
24	partially differentiable	11.7%
14	convex	6.8%
11	controversial	5.4%
5	has_noise	2.4%
5	highly multimodal	2.4%
4	deceptive	2.0%
4	ill-conditioned	2.0%
3	finiteatinf	1.5%
3	partially separable	1.5%

Total distinct properties: 18

Available Properties

The package defines the following valid properties:

Property	Description	Common Examples
bounded	Finite box constraints (`lb` and `ub` are defined and finite)	beale, branin, michalewicz
continuous	Continuous everywhere in the domain	Most functions
controversial	Global minimum or value debated in literature	langermann
convex	Convex (unique global minimum)	sphere, quadratic
deceptive	Designed to mislead certain optimizers	Rare
differentiable	Differentiable everywhere	rosenbrock, ackley
finiteatinf	Function value remains finite as variables → ±∞	Rare
fully non-separable	Completely non-separable (strong interactions)	Rare
has_constraints	Additional constraints beyond box bounds	Rare in this package
has_noise	Stochastic noise in evaluation	quartic (noisy variants)
highly multimodal	Very large number of local minima	rastrigin, weierstrass
multimodal	Multiple local minima	branin, eggholder
non-convex	Not convex	ackley, rosenbrock
non-separable	Variables are coupled	rosenbrock, ackley
partially differentiable	Differentiable almost everywhere	bartelsconn
partially separable	Some variables independent	Rare
quasi-convex	Quasi-convex	Rare
scalable	Defined for arbitrary dimension n ≥ 2	rosenbrock, rastrigin
separable	Fully separable (optimize each variable independently)	sphere, sumofpowers
strongly convex	Strongly convex	quadratic
unimodal	Single global minimum (no local minima)	sphere
ill-conditioned	Poorly conditioned Hessian (slow convergence)	rosenbrock

Only these properties are allowed. Adding new ones requires extending VALID_PROPERTIES and updating tests.

Accessing Properties

Use dedicated accessor functions – never access tf.meta[:properties] directly.

Primary Accessor

property(tf::TestFunction, prop::AbstractString) -> Bool

Returns true if the property is present.
Throws clear error for invalid names.

Example: property(tf, "multimodal") # → true or false

Convenience Shortcuts

bounded(tf) -> Bool scalable(tf) -> Bool differentiable(tf) -> Bool multimodal(tf) -> Bool separable(tf) -> Bool

List All Properties

properties(tf::TestFunction) -> Vector{String}

Returns sorted vector of all properties (alphabetical order).

Example: properties(tf)

→ ["bounded", "continuous", "differentiable", "multimodal", "non-convex", "non-separable"]

Filtering Functions by Property

The package provides a helper for easy filtering:

filter_testfunctions(predicate) -> Vector{TestFunction}

Examples:

All bounded functions

boundedfuncs = filtertestfunctions(bounded)

All multimodal functions

multimodalfuncs = filtertestfunctions(multimodal)

Bounded AND scalable functions

boundedscalable = filtertestfunctions(tf -> bounded(tf) && scalable(tf))

Highly multimodal functions

highlymultimodal = filtertestfunctions(tf -> property(tf, "highly multimodal"))

All convex functions

convexfuncs = filtertestfunctions(tf -> convex(tf))

This is the recommended way to explore or benchmark subsets of the collection.

Other Metadata Accessors

Accessor	Returns	Notes
name(tf)	String (function name)	Direct field access
dim(tf)	Int or -1 (if scalable)	-1 means arbitrary dimension
start(tf, n=nothing)	Vector{Float64} (start point)	Requires n for scalable
min_position(tf, n=nothing)	Vector{Float64} (global minimizer)	Requires n for scalable
min_value(tf, n=nothing)	Float64 (global minimum value)	Requires n for scalable
lb(tf, n=nothing)	Vector{Float64} (lower bounds)	Requires n for scalable
ub(tf, n=nothing)	Vector{Float64} (upper bounds)	Requires n for scalable
source(tf)	String (literature reference or "Unknown Source")	Fallback if missing

These accessors handle scalable functions automatically (pass n when needed).

Design Philosophy

Consistency enforced: Test suite checks logical implications and incompatibilities (e.g., convex cannot coexist with multimodal).
No raw metadata access: Use accessors for future-proofing and clarity.
Extensible: New properties can be added by updating VALID_PROPERTIES and tests.

For questions or to suggest new properties/functions, open an issue on the repository.