Complexity iteration analysis for strongly convex multi-objective optimization using a Newton path-following procedure

Embargo End Date
2021-07-23

Type
Article

Authors
Bergou, El Houcine
Diouane, Youssef
Kungurtsev, Vyacheslav

KAUST Department
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Online Publication Date
2020-07-23

Print Publication Date
2021-06

Date
2020-07-23

Submitted Date
2020-03-07

Abstract
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.

Citation
Bergou, E.-H., Diouane, Y., & Kungurtsev, V. (2020). Complexity iteration analysis for strongly convex multi-objective optimization using a Newton path-following procedure. Optimization Letters. doi:10.1007/s11590-020-01623-x

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”.

Publisher
Springer Nature

Journal
Optimization Letters

DOI
10.1007/s11590-020-01623-x

arXiv
2004.02979

Additional Links
http://link.springer.com/10.1007/s11590-020-01623-x

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