A Tikhonov-regularized inertial dynamical system for convex multiobjective optimization converges fast to weak Pareto optimal points, with strong convergence to a minimum-norm solution in the main regime.
Multiibjective optimization : an inertial dynamical approach to Pareto optima
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abstract
We present some first results concerning a gradient-based dynamic approach to multi-objective optimization problems, involving inertial effects. We prove the existence of global solution trajectories for this second-order differential equation, and their convergence to weak Pareto points in the convex case. It is a first step towards the design of fast numerical methods for multi-objective optimization.
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2024 1verdicts
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Inertial dynamics with vanishing Tikhonov regularization for multiobjective optimization
A Tikhonov-regularized inertial dynamical system for convex multiobjective optimization converges fast to weak Pareto optimal points, with strong convergence to a minimum-norm solution in the main regime.