报告主题：Stochastic Proximal Quasi-Newton methods for Nonconvex Composite Optimization
报告人：袁亚湘 院士 （中科院数学与系统科学研究院）
报告时间：2018年 6月4日（周一）9:45
报告地点：校本部G507
邀请人：白延琴
报告摘要：In this talk, we propose a generic algorithmic framework for proximal stochastic quasi-Newton (SPQN) methods to solve nonconvex composite optimization problems. Stochastic second-order information is explored to construct proximal subproblem. Under mild conditions we show the non-asympotic convergence of the proposed algorithm to stationary point of original problems and analyze its computational complexity. Besides, we extend the proximal form of Polyak-$\L$ojasiewicz (PL) inequality to constrained settings and obtain the constrained proximal PL (CP-PL) inequality. Under CP-PL inequality linear convergence rate of the proposed algorithm is achieved. Moreover, we propose a modified self-scaling symmetric rank one (MSSR1) incorporated in the framework for SPQN method, which is called stochastic symmetric rank one (StSR1) method. Finally, we report some numerical experiments to reveal the effectiveness of the proposed algorithm.
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