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

Bergou, El Houcine and Diouane, Youssef and Kungurtsev, Vyacheslav Complexity iteration analysis for strongly convex multi-objective optimization using a Newton path-following procedure. (2020) Optimization Letters. ISSN 1862-4472

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Official URL: https://doi.org/10.1007/s11590-020-01623-x

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.

Item Type:Article
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:French research institutions > Institut national de recherche pour l'agriculture, l'alimentation et l'environnement - INRAE (FRANCE)
Université de Toulouse > Institut Supérieur de l'Aéronautique et de l'Espace - ISAE-SUPAERO (FRANCE)
Other partners > King Abdullah University of Science and Technology - KAUST (SAUDI ARABIA)
Other partners > Czech Technical University in Prague - CTU (CZECH REPUBLIC)
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Deposited On:28 Jul 2020 12:33

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