Non-linear optimization method for maximum point search in functions with corner or cusp points

A function is non-differentiable when there is a cusp or a corner point in its graph. To solve this problem we propose a nonlinear optimization model whose objective function is the Euclidean distance function. To identify the maximum points of a function that has corner or cusp points, according to the proposed model, a series of segments are generated which are measured through the Euclidean distance, which are all perpendicular to the abscissa axis. Therefore, by maximizing the Euclidean distance it is possible to identify the segment whose points represent the maximum of the function and its projection on the abscissa axis. The proposed model therefore wants to be an alternative to maximum point search methods in the presence of functions that have points of non-derivability. The proposed method and the consequent model are going to be applied in financial issues connected to the analysis of some stock exchange trends and connected markets’ behaviors. This occasion is useful to present the mathematical approach and structure to a qualified audience in getting important feed-backs in terms of comments, remarks, potential ideas of suitable applications.