marinepredator (version 0.0.1)

F02: Sum of Absolute Values and Products (F02)

Description

A unimodal test function that combines the sum of absolute values and the product of absolute values.

Usage

F02(x)

Value

Numeric scalar representing the function value.

Arguments

x

Numeric vector of input values.

Details

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

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

Characteristics:

• Type: Unimodal

• Separable: No (due to product term)

• Differentiable: No (at points where any x_i = 0)

• Convex: Yes

• Default bounds: \([-10, 10]^n\)

• Default dimensions: 50

See Also

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

Examples

F02(c(0, 0))      # Returns 0 (global minimum)
F02(c(1, 2))      # Returns |1| + |2| + |1|*|2| = 1 + 2 + 2 = 5
F02(c(-1, -2))    # Returns 1 + 2 + 2 = 5