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

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.
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https://hal.inrae.fr/hal-03285165
Contributor : Roselyne Tâche <>
Submitted on : Tuesday, July 13, 2021 - 10:34:32 AM
Last modification on : Saturday, July 17, 2021 - 3:50:34 AM

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El-Houcine Bergou, Youssef Diouane, Vyacheslav Kungurtsev. Complexity iteration analysis for strongly convex multi-objective optimization using a Newton path-following procedure. Optimization Letters, Springer Verlag, 2021, 15 (4), pp.1215-1227. ⟨10.1007/s11590-020-01623-x⟩. ⟨hal-03285165⟩

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