学术报告

An inexact proximal augmented Lagrangian framework with arbitrary linearly convergent inner.......

发布人：发布时间： 2019-12-20

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**题目：**An inexact proximal augmented Lagrangian framework with arbitrary linearly convergent inner solver for composite convex optimization

**报告人：**Zheng Qu (University of Hong Kong)

**摘要：**We propose an inexact proximal augmented Lagrangian framework with explicit inner problem termination rule for composite convex optimization problems. We consider arbitrary linearly convergent inner solver including in particular stochastic algorithms, making the resulting framework more scalable facing the ever-increasing problem dimension. Each subproblem is solved inexactly with an explicit and self-adaptive stopping criterion, without requiring to set an a priori target accuracy. When the primal and dual domain are bounded, our method achieves the best known complexity bounds in terms of number of inner solver iterations, respectively for the strongly convex and non-strongly convex case. Without the boundedness assumption, only logarithm terms need to be added. Within the general framework that we propose, we also obtain the first iteration complexity bounds under relative smoothness assumption on the differentiable component of the objective function. We show through theoretical analysis as well as numerical experiments the computational speedup achieved by the use of randomized inner solvers for large-scale problems.

**时间: **2019 年 12 月 23 日 16:00-17:30

**地点: **南京大学鼓楼校区西大楼 210

**报告人简介：**

Zheng Qu obtained her Ph.D. in 2013 at Centre des Math´ematiques Appliqu´ees, Ecole Polytechnique, France. Her thesis was on attenuation of the curse of dimensionality in the numerical solution of HJB equations and nonlinear Perron Frobenius theory, under the supervision of Prof. Stephane Gaubert. From 2014 to 2015 she was a postdoc in the Department of Mathematics at the University of Edinburgh, where she worked with Prof. Peter Richtarik on randomized coordinate descent methods for large scale optimization. Since 2015 she holds

a position of Assistant Professor at the University of Hong Kong and work on large-scale programming from both theoretical and algorithmic aspects.

**邀请人：**顾国勇老师、杨俊锋老师