Graph algorithm for partially-linear problems obtained by absolute value functions

Abstract

The increasing interest in partially-linear models is caused by their role in economics, technology and mathematics. Every continuous partially-linear function with a finite number of linear parts can be formulated by means of linear function and absolute value functions. If we presebt every absolote value function as vertex of a graph we obtain the graph interpretaion of this optimization problem. The Partially-linear problems are often not only nondifferentiable but nonconvex as well,which makes their solving by standard optimization methods difficult. In this work we give the necessary and sufficient conditions for local optimality. An algorithm for solving such problems, based on the constructive optimization methods is suggested.