Application of Particle Swarm Optimization in Figuring out Non-differentiable Point of Function

Abstract

Owing to the importance of non-differentiable point in a function for economy, engineering and theoretical analysis, this paper brings forward a novel methodology to figure out the non-differentiable point of function which is based on adjusting the models for global extremum and local extremum of particle swarm optimazation (PSO). The algorithm takes the difference between left and right difference quotients as the adaptive value of the particle. By them, it defines local extremum and global extremum for PSO and makes particle close to non-differentiable point of target function, and then figures the point out. The validity of the algorithm is verified by the result of numerical calculation.