In this note, we consider the iteration complexity of solving strongly convex multi-objective optimization problems. We discuss the precise meaning of this problem, noting that its definition is ambiguous, and focus on the most natural notion of finding a set of Pareto optimal points across a grid of scalarized problems. We prove that, in most cases, performing sensitivity based path-following after obtaining one solution is the optimal strategy for this task in terms of iteration complexity.
Bibliographical noteKAUST Repository Item: Exported on 2020-10-01
Acknowledgements: We would like to thank two anonymous referees for their careful readings and corrections that helped us to improve our manuscript significantly. E. Bergou received support from the AgreenSkills+ fellowship programme which has received funding from the EU’s Seventh Framework Programme under Grant Agreement No. FP7-609398 (AgreenSkills+ contract). V. Kungurtsev received support from the OP VVV Project CZ.02.1.01/0.0/0.0/16_019/0000765 “Research Center for Informatics”.