The Mixing method: coordinate descent for low-rank semidefinite programming

A Coordinate Ascent Method for Solving Semidefinite Relaxations of Non-convex Quadratic Integer Programs

We present a coordinate ascent method for a class of semidefinite programming problems that arise in non-convex quadratic integer optimization. These semidefinite programs are characterized by a small total number of active constraints and by low-rank constraint matrices. We exploit this special structure by solving the dual problem, using a barrier method in combination with a coordinate-wise ...

Efficient Low-Rank Stochastic Gradient Descent Methods for Solving Semidefinite Programs

We propose a low-rank stochastic gradient descent (LR-SGD) method for solving a class of semidefinite programming (SDP) problems. LR-SGD has clear computational advantages over the standard SGD peers as its iterative projection step (a SDP problem) can be solved in an efficient manner. Specifically, LR-SGD constructs a low-rank stochastic gradient and computes an optimal solution to the project...

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...

A Convergent Gradient Descent Algorithm for Rank Minimization and Semidefinite Programming from Random Linear Measurements

We propose a simple, scalable, and fast gradient descent algorithm to optimize a nonconvex objective for the rank minimization problem and a closely related family of semidefinite programs. With O(rκn log n) random measurements of a positive semidefinite n×nmatrix of rank r and condition number κ, our method is guaranteed to converge linearly to the global optimum.

Block coordinate descent methods for semidefinite programming