An interior point method for linearly constrained multiobjective optimization based on suitable descent directions

The aim of this paper is the development of an algorithm to find the critical points of a linearly constrained multiobjective optimization problem. The proposed algorithm is an interior point method based on suitable directions that play the role of projected gradient-like directions for the vector objective function. The method does not rely on an "a priori" scalarization of the vector objective function and is based on a dynamic system defined by a vector field of descent directions in the feasible region. We prove that the limit points of the solutions of the system satisfy the Karush-Kuhn-Tucker (KKT) first order necessary condition for the linearly constrained multiobjective optimization problem. The algorithm has been tested on some linearly constrained optimization problems and the numerical results obtained show that the algorithm approximates satisfactory the whole (weakly) local optimal Pareto set.