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

El Houcine Bergou, Youssef Diouane, Vyacheslav Kungurtsev

Research output: Contribution to journalArticlepeer-review

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.
Original languageEnglish (US)
JournalOptimization Letters
DOIs
StatePublished - Jul 23 2020

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