This talk is dedicated to smooth, convex multiobjective optimization problems defined in a general Hilbert space setting. While accelerated first-order methods are popular in singleobjective optimization, these methods have not been sufficiently studied for multiobjective optimization problems. A fruitful approach to analyze gradient methods is to interpret them as discretizations of appropriate dynamical systems. The analysis of the continuous dynamics is often simpler and can later on be transferred to the discrete domain. This perspective is not fully exploited in multiobjective optimization.

In this talk, we present contributions to the study of accelerated multiobjective gradient methods. We introduce a novel inertial gradient-like dynamical system with asymptotic vanishing damping in the multiobjective setting. The trajectories of this system converge weakly to weak Pareto optimal solutions to the multiobjective optimization problem. The values of the objective functions converge to the optimal value at a rate of O(1/t^2). The discretization of this system leads to an accelerated multiobjective gradient method. For this method we prove convergence of the function values with a rate of O(1/k^2), while the convergence of the iterates remains an open question for now.