Non-Linear Optimization Method for Maximum Point Search in Functions with Corner or Cusp Points

Abstract

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 could be an alternative to maximum point search methods in the presence of functions that have points of non-derivability.

Keywords

• non-linear problem
• optimization
• non-derivability