---
res:
bibo_abstract:
- We derive efficient algorithms to compute weakly Pareto optimal solutions for
smooth, convex and unconstrained multiobjective optimization problems in general
Hilbert spaces. To this end, we define a novel inertial gradient-like dynamical
system in the multiobjective setting, which trajectories converge weakly to Pareto
optimal solutions. Discretization of this system yields an inertial multiobjective
algorithm which generates sequences that converge weakly to Pareto optimal solutions.
We employ Nesterov acceleration to define an algorithm with an improved convergence
rate compared to the plain multiobjective steepest descent method (Algorithm 1).
A further improvement in terms of efficiency is achieved by avoiding the solution
of a quadratic subproblem to compute a common step direction for all objective
functions, which is usually required in first-order methods. Using a different
discretization of our inertial gradient-like dynamical system, we obtain an accelerated
multiobjective gradient method that does not require the solution of a subproblem
in each step (Algorithm 2). While this algorithm does not converge in general,
it yields good results on test problems while being faster than standard steepest
descent.@eng
bibo_authorlist:
- foaf_Person:
foaf_givenName: Konstantin
foaf_name: Sonntag, Konstantin
foaf_surname: Sonntag
foaf_workInfoHomepage: http://www.librecat.org/personId=56399
orcid: https://orcid.org/0000-0003-3384-3496
- foaf_Person:
foaf_givenName: Sebastian
foaf_name: Peitz, Sebastian
foaf_surname: Peitz
foaf_workInfoHomepage: http://www.librecat.org/personId=47427
orcid: 0000-0002-3389-793X
bibo_doi: 10.1007/s10957-024-02389-3
dct_date: 2024^xs_gYear
dct_language: eng
dct_publisher: Springer@
dct_title: Fast Multiobjective Gradient Methods with Nesterov Acceleration via Inertial
Gradient-Like Systems@
...