Complex optimization algorithms
The nature of the objective function helps select the algorithm to be considered for the optimization of a given business problem. The more information that is available about the function, the easier it is to optimize the function. Of most importance is the fact that the objective function can be differentiated at any point in the search space.
Differentiability of objective functions
A differentiable objective function is one for which the derivative can be calculated at any given point in input space. The derivative (slope) is the rate of change of the function at that point. The Hessian is the rate at which the derivative of the function changes. Calculus helps optimize simple differentiable functions analytically. For differentiable objective functions, gradient-based optimization algorithms are used. However, there are objective functions for which the derivative cannot be computed, typically for very complex (noisy, multimodal, etc.) functions...
