Regularization Methods for Semidefinite Programming

Regularization Methods for Semidefinite Programming

We introduce a new class of algorithms for solving linear semidefinite programming (SDP) problems. Our approach is based on classical tools from convex optimization such as quadratic regularization and augmented Lagrangian techniques. We study the theoretical properties and we show that practical implementations behave very well on some instances of SDP having a large number of constraints. We ...

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...

Row by row methods for semidefinite programming

We present a row-by-row (RBR) method for solving semidefinite programming (SDP) problem based on solving a sequence of problems obtained by restricting the n-dimensional positive semidefinite constraint on the matrix X. By fixing any (n − 1)-dimensional principal submatrix of X and using its (generalized) Schur complement, the positive semidefinite constraint is reduced to a simple second-order...

Block coordinate descent methods for semidefinite programming

Efficient First-order Methods for Linear Programming and Semidefinite Programming

The study of first-order methods has largely dominated research in continuous optimization for the last decade, yet still the range of problems for which “optimal” first-order methods have been developed is surprisingly limited, even though much has been achieved in some areas with high profile, such as compressed sensing. Even if one restricts attention to, say, linear programming, the problem...