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Digitale Infotage für Schüler*innen vom 06.-09. Februar 2023

Photo: Universität Paderborn, Adelheid Rutenburges

Konstantin Sonntag, MSc

 Konstantin Sonntag, MSc

Institut für Industriemathematik

Member - Research Associate

Chair of Applied Mathematics

Member - Research Associate

Data Science for Engineering

Member - Research Student

+49 5251 60-4487
Technologiepark 21
33100 Paderborn

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Fast Multiobjective Gradient Methods with Nesterov Acceleration via Inertial Gradient-like Systems

K. Sonntag, S. Peitz, in: arXiv:2207.12707, 2022

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, whose 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 by two to three orders of magnitude.

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