TY - JOUR
T1 - Convergence Rate of Gradient Descent Method for Multi-Objective Optimization
AU - Zeng , Liaoyuan
AU - Dai , Yuhong
AU - Huang , Yakui
JO - Journal of Computational Mathematics
VL - 5
SP - 689
EP - 703
PY - 2019
DA - 2019/03
SN - 37
DO - http://doi.org/10.4208/jcm.1808-m2017-0214
UR - https://global-sci.org/intro/article_detail/jcm/13041.html
KW - Multi-objective optimization, Gradient descent, Convergence rate.
AB - <p style="text-align: justify;">The convergence rate of the gradient descent method is considered for unconstrained
multi-objective optimization problems (MOP). Under standard assumptions, we prove that
the gradient descent method with constant step sizes converges sublinearly when the objective functions are convex and the convergence rate can be strengthened to be linear if
the objective functions are strongly convex. The results are also extended to the gradient descent method with the Armijo line search. Hence, we see that the gradient descent
method for MOP enjoys the same convergence properties as those for scalar optimization.</p>