Geometry-Aware Multi-Objective Optimization: Norm-Constrained Oracles with Entropic Weight Updates
This work introduces a single-loop method for multi-objective optimization that combines a norm-constrained linear minimization oracle with entropic updates of task weights. It achieves strong convergence rates in arbitrary norm pairs, providing ergodic stationarity and iteration-wise inner-gap control, making it robust for complex, non-Euclidean optimization problems.