Complexity bound of trust-region methods for convex smooth unconstrained multiobjective optimization

In this paper, we analyze the worst-case complexity of trust-region methods for solving unconstrained smooth multiobjective optimization problems. We particularly focus on the method proposed by Villacorta et al. [J Optim Theory Appl 160:865889, 2014]. When the component functions are convex (respectively strongly convex), we will derive a complexity bound of O(epsilon(-1)) (respectively O(log epsilon(-1))) for driving some criticality measure below some given positive epsilon. The derived complexity bounds recover those of classical trust-region methods for solving (strongly) convex smooth unconstrained single-objective problems.