marinepredator (version 0.0.1)

F01: Sphere Function (F01)

Description

The Sphere function is a simple unimodal test function commonly used to evaluate the performance of optimization algorithms. It has a single global minimum at the origin.

Usage

F01(x)

Value

Numeric scalar representing the function value.

Arguments

x

Numeric vector of input values.

Details

Formula: $$f(x) = \sum_{i=1}^{n} x_i^2$$

Global minimum: \(f(0, 0, ..., 0) = 0\)

Characteristics:

• Type: Unimodal

• Separable: Yes

• Differentiable: Yes

• Convex: Yes

• Default bounds: \([-100, 100]^n\)

• Default dimensions: 50

See Also

test-functions for an overview of all test functions, get_function_details to retrieve function parameters.

Examples

F01(c(0, 0, 0))    # Returns 0 (global minimum)
F01(c(1, 2, 3))    # Returns 1 + 4 + 9 = 14
F01(rep(0, 50))    # Returns 0 in 50 dimensions