Multiobjective Conjugate Gradient Methods on Riemannian Manifolds

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

Journal of Optimization Theory and Applications, 2023, vol. 197, issue 3, No 14, 1229-1248

Abstract: Abstract In this paper, we present the multiobjective optimization methods of conjugate gradient on Riemannian manifolds. The concepts of optimality and Wolfe conditions, as well as Zoutendijk’s theorem, are redefined in this setting. We show that under some standard assumptions, a sequence generated by these algorithms converges to a critical Pareto point. This is when the step sizes satisfy the multiobjective Wolfe conditions. In particular, we propose the Fletcher–Reeves, Dai–Yuan, Polak–Ribière–Polyak, and Hestenes–Stiefel parameters and further analyze the convergence behavior of the first two methods and test their performance against the steepest descent method.

Keywords: Multiobjective optimization; Multicriteria optimization; Pareto optimality; Riemannian manifolds; Conjugate gradient methods; Wolfe conditions (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10957-023-02224-1

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