Multiobjective BFGS method for optimization on Riemannian manifolds

Shahabeddin Najafi () and Masoud Hajarian ()
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Shahabeddin Najafi: Shahid Beheshti University
Masoud Hajarian: Shahid Beheshti University

Computational Optimization and Applications, 2024, vol. 87, issue 2, No 1, 337-354

Abstract: Abstract This paper introduces a Riemannian BFGS method to address multiobjective optimization problems with strongly retraction-convex objective functions. This method is a natural extension of the Euclidean version and produces a sequence of iterates that converges to a Pareto optimal point regardless of the initial point. The main component of our globalization strategy is a generalized Wolfe line search. Numerical experiments demonstrate the superiority and effectiveness of the proposed algorithm.

Keywords: Multiobjective optimization; Multicriteria optimization; Riemannian manifolds; Pareto optimality; BFGS quasi-Newton; Wolfe conditions (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10589-023-00522-y

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