DeepAI AI Chat
Log In Sign Up

Bundle Method Sketching for Low Rank Semidefinite Programming

by   Lijun Ding, et al.
cornell university

In this paper, we show that the bundle method can be applied to solve semidefinite programming problems with a low rank solution without ever constructing a full matrix. To accomplish this, we use recent results from randomly sketching matrix optimization problems and from the analysis of bundle methods. Under strong duality and strict complementarity of SDP, we achieve Õ(1/ϵ) convergence rates for both the primal and the dual sequences, and the algorithm proposed outputs a O(√(ϵ)) approximate solution X̂ (measured by distances) with a low rank representation with at most Õ(1/ϵ) many iterations.


page 1

page 2

page 3

page 4


Barrier and penalty methods for low-rank semidefinite programming with application to truss topology design

The aim of this paper is to solve large-and-sparse linear Semidefinite P...

On the regularity and conditioning of low rank semidefinite programs

Low rank matrix recovery problems appear widely in statistics, combinato...

Local convergence of alternating low-rank optimization methods with overrelaxation

The local convergence of alternating optimization methods with overrelax...

Graph Coloring and Semidefinite Rank

This paper considers the interplay between semidefinite programming, mat...

Primal-Dual Block Frank-Wolfe

We propose a variant of the Frank-Wolfe algorithm for solving a class of...

Dual Convexified Convolutional Neural Networks

We propose the framework of dual convexified convolutional neural networ...

Robust Learning from Noisy Side-information by Semidefinite Programming

Robustness recently becomes one of the major concerns among machine lear...