A Trust Region Method for Solving Multicriteria Optimization Problems on Riemannian Manifolds

We extend and analyze the trust region method for solving smooth and unconstrained multicriteria optimization problems on Riemannian manifolds. At each iteration of this method, a quadratic model is assigned to each component of the vectorial objective function by considering the notion of retractions. Then, a subproblem is constructed and solved to find a new descent direction. Furthermore, we investigate the convergence behavior of the algorithm by considering radially Lipschitz continuously differentiable functions. In the end, the algorithm is implemented on three examples, and the corresponding numerical results showing the efficiency of the proposed method are reported as well.