We propose a new approach for constructing practical algorithms for solving smooth multiobjective optimization problems based on determining decreasing directions via suitable linear programming problems. The presented iterative method is specialized for unconstrained, sign constrained and linearly constrained multiobjective optimization problems. In all cases, the objective function values sequence is decreasing with respect to the corresponding nonnegative orthant, and every accumulation point of the sequence generated by the algorithm is a substationary point to the considered multiobjective optimization problem, becoming, under convexity assumptions, a weakly Pareto efficient solution. Different to similar algorithms from the literature, the ones proposed in this work involve decreasing directions that are easily computable in polynomial time.
The talk is based on joint work with Tibor Illés and Petra Renáta Rigó (Corvinus Center for Operations Research at Corvinus Institute for Advanced Studies, Corvinus University of Budapest).