Sum of Absolute Values and Products (F02)

Source: R/F02.R

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

F02(x)

Arguments

x

Numeric vector of input values.

Value

Numeric scalar representing the function value.

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)
#> [1] 0
F02(c(1, 2))      # Returns |1| + |2| + |1|*|2| = 1 + 2 + 2 = 5
#> [1] 5
F02(c(-1, -2))    # Returns 1 + 2 + 2 = 5
#> [1] 5