We propose a steepest descent method for unconstrained multicriteria optimization and a "feasible descent direction" method for the constrained case. In the unconstrained case, the objective functions are assumed to be continuous differentiable. In the constrained case, objective and constraint functions are assumed to be Lipshitz-continuous differentiable and a constraint qualification is assumed. Under these conditions, it is shown that these methods converge to a point satisfying certain first-order necessary conditions for Pareto-optimality. Both methods do not scalarize the original vector-optimization problem. Neither ordering information nor weighting factors for the different objective functions are assumed to be known. In the single objective case, we retrieve the Steepest descent method and Zoutendijk's method of feasible directions, respectively.

Keywords: Multicriteria optimization, multi-objective programming, vector optimization, Pareto points, steepest descent.