The aim of this manuscript is to characterize the continuity properties of the multiobjective steepest descent direction for smooth objective functions. We will show that this direction is Holder continuous with optimal exponent 1/2. In particular, this direction fails to be Lipschitz continuous even for polynomial objectives.
Cite
@article{arxiv.1802.01402,
title = {Holder continuity of the steepest descent direction for multiobjective optimization},
author = {Benar Fux Svaiter},
journal= {arXiv preprint arXiv:1802.01402},
year = {2018}
}