BILGO: Bilateral greedy optimization for large scale semidefinite programming

BILGO: Bilateral greedy optimization for large scale semidefinite programming

Many machine learning tasks (e.g. metric and manifold learning problems) can be formulated as convex semidefinite programs. To enable the application of these tasks on a large-scale, scalability and computational efficiency are considered desirable properties for a practical semidefinite programming algorithm. In this paper, we theoretically analyse a new bilateral greedy optimization(denoted B...

Practical first order methods for large scale semidefinite programming

This paper investigates first order methods for solving large scale semidefinite programs. While interior point methods are (a) theoretically sound and (b) effective and robust in practice, they are only practical for small scale problems. As the dimension of the problem increases, both the space and time needed become prohibitive. We survey first order methods which have been proposed in the l...

Graph Laplacian Regularization for Large-Scale Semidefinite Programming

In many areas of science and engineering, the problem arises how to discover low dimensional representations of high dimensional data. Recently, a number of researchers have converged on common solutions to this problem using methods from convex optimization. In particular, many results have been obtained by constructing semidefinite programs (SDPs) with low rank solutions. While the rank of ma...

Sparse Semidefinite Programming Relaxations for Large Scale Polynomial Optimization and Their Applications to Differential Equations

Solving Large-Scale Sparse Semidefinite Programs for Combinatorial Optimization

We present a dual-scaling interior-point algorithm and show how it exploits the structure and sparsity of some large scale problems. We solve the positive semideenite relaxation of combinatorial and quadratic optimization problems subject to boolean constraints. We report the rst computational results of interior-point algorithms for approximating the maximum cut semideenite programs with dimen...