marinepredator (version 0.0.1)

F03: Sum of Squared Cumulative Sums (F03)

Description

A unimodal test function that calculates the sum of squared cumulative sums, also known as the Schwefel 2.22 variant.

Usage

F03(x)

Value

Numeric scalar representing the function value.

Arguments

x

Numeric vector of input values.

Details

Formula: $$f(x) = \sum_{i=1}^{n} \left(\sum_{j=1}^{i} x_j\right)^2$$

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

Characteristics:

• Type: Unimodal

• Separable: No

• Differentiable: Yes

• Convex: Yes

• Default bounds: \([-100, 100]^n\)

• Default dimensions: 50

This function is non-separable because each term depends on all previous variables, making it useful for testing algorithms' ability to handle variable dependencies.

See Also

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

Examples

F03(c(0, 0, 0))    # Returns 0 (global minimum)
F03(c(1, 2, 3))    # Returns 1^2 + (1+2)^2 + (1+2+3)^2 = 1 + 9 + 36 = 46