P000041
Stochastic Trust Region Methods with Trust Region Radius Depended on Probabilistic Models
*Xiaoyu Wang (Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences & University of Chinese Academy of Sciences)
Ya-xiang Yuan (State Key Laboratory of Scientific/Engineering Computing, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences)
We present a generic stochastic trust region scheme in which the trust region
radius is directly associated with the random model. The proposed scheme is
analyzed based on random models and random estimates of the objective function
with certain probability provided some assumptions are satisfied. Especially, we show
a specific algorithm STRME in which the trust region radius is linearly correlated
with the 2-norm of the stochastic gradient. Moreover, the convergence complexity
of STRME method in nonconvex, convex and strongly convex settings have all been
analyzed. In the end, some numerical experiments are carried out to reveal the benefits
of the proposed methods compared to the existing stochastic trust region methods
and other related stochastic gradient methods.