Optimization model with nonconvex monotone piecewise linear objective function

The paper describes new approach to solution of some optimization models with non-convex piecewise linear objective function with monotone course. The matter of non-convexity complicates searching for an optimal solution of an optimization problem. We propose computationally tractable algorithm based on multiobjective optimization, capable of solving some non-convex optimization problems. The class of the optimization problems we deal with is specified and written as a mathematical model. The model is then transformed into appropriate form with the help of additional linear constraints. When piecewise linear functions are present, the search space represented here by convex polytope has some interesting properties we describe before the algorithm itself. The algorithm is proposed on the basis of multiobjective simplex algorithm.