Complexity analysis of primal-dual interior-point methods for semidefinite optimization based on a parametric kernel function with a trigonometric barrier term

Guoqiang Wang, ,Zhongtuan Zheng,Xinzhong Cai,Zhongchen Wu

doi:10.3934/naco.2015.5.101

Abstract

In this paper, we present a class of large- and small-update primal-dual interior-point methods forsemidefinite optimization based on a parametric kernel function with a trigonometric barrier term.For both versions of the kernel-based interior-point methods, the worst case iteration bounds are established, namely,$O(n^{\frac{2}{3}}\log\frac{n}{\varepsilon})$ and $O(\sqrt{n}\log\frac{n}{\varepsilon})$, respectively.These results match the ones obtained in the linear optimization case.

Highlights

Summary: In this paper, we propose an efficient and scalable low rank matrix completion algorithm
We further propose an economic version of our algorithm by introducing a novel weight updating rule to reduce the time and storage complexity
Both versions are computationally inexpensive for each matrix pursuit iteration and find satisfactory results in a few iterations

Summary

Introduction

Summary: In this paper, we propose an efficient and scalable low rank matrix completion algorithm. The key idea is to extend the orthogonal matching pursuit method from the vector case to the matrix case.

Results

Conclusion