Paper Info
Title
Bundle-level type methods uniformly optimal for smooth and nonsmooth convex optimization
Abstract
The main goal of this paper is to develop uniformly optimal first-order methods for convex programming (CP). By uniform optimality we mean that the first-order methods themselves do not require the input of any problem parameters, but can still achieve the best possible iteration complexity bounds. By incorporating a multi-step acceleration scheme into the well-known bundle-level method, we develop an accelerated bundle-level method, and show that it can achieve the optimal complexity for solving a general class of black-box CP problems without requiring the input of any smoothness information, such as, whether the problem is smooth, nonsmooth or weakly smooth, as well as the specific values of Lipschitz constant and smoothness level. We then develop a more practical, restricted memory version of this method, namely the accelerated prox-level (APL) method. We investigate the generalization of the APL method for solving certain composite CP problems and an important class of saddle-point problems recently studied by Nesterov (Math Program 103:127---152, 2005). We present promising numerical results for these new bundle-level methods applied to solve certain classes of semidefinite programming and stochastic programming problems.
Year
DOI
Venue
2015
10.1007/s10107-013-0737-x
Math. Program.
Keywords
Field
DocType
bundle-level,90c25,convex programming,62l20,complexity,optimal methods,90c15,68q25
Saddle,Discrete mathematics,Mathematical optimization,Random coordinate descent,Lipschitz continuity,Smoothness,Stochastic programming,Convex optimization,Bundle,Mathematics,Semidefinite programming
Journal
Volume
Issue
ISSN
149
1-2
1436-4646
Citations 
PageRank 
References 
9
0.60
26
Authors
1
Name
Order
Citations
PageRank
Guanghui Lan1121266.26