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- Title
Multi-objective Variational Curves.
- Authors
Kaya, C. Yalçın; Noakes, Lyle; Zhang, Erchuan
- Abstract
Riemannian cubics in tension are critical points of the linear combination of two objective functionals, namely the squared L 2 norms of the velocity and acceleration of a curve on a Riemannian manifold. We view this variational problem of finding a curve as a multi-objective optimization problem and construct the Pareto fronts for some given instances where the manifold is a sphere and where the manifold is a torus. The Pareto front for the curves on the torus turns out to be particularly interesting: the front is disconnected and it reveals two distinct Riemannian cubics with the same boundary data, which is the first known nontrivial instance of this kind. We also discuss some convexity conditions involving the Pareto fronts for curves on general Riemannian manifolds.
- Subjects
RIEMANNIAN manifolds; ACCELERATION (Mechanics); TORUS; CURVES; FUNCTIONALS
- Publication
Journal of Optimization Theory & Applications, 2024, Vol 201, Issue 2, p955
- ISSN
0022-3239
- Publication type
Article
- DOI
10.1007/s10957-024-02427-0