39 citations · 143 across the 11 of their papers we have counts for
7 papers · 1 filter
Polynomial time guarantees for the Burer-Monteiro method
Diego Cifuentes, Ankur Moitra
The Burer-Monteiro method is one of the most widely used techniques for solving large-scale semidefinite programs (SDP). The basic idea is to solve a nonconvex program in , wher…
A convex relaxation to compute the nearest structured rank deficient matrix
Diego Cifuentes
Given an affine space of matrices and a matrix , consider the problem of computing the closest rank deficient matrix to on with re…
On the Burer-Monteiro method for general semidefinite programs
Diego Cifuentes
Consider a semidefinite program (SDP) involving an positive semidefinite matrix . The Burer-Monteiro method uses the substitution to obtain a nonconvex opt…
Sums of squares in Macaulay2
Diego Cifuentes, Thomas Kahle, Pablo A. Parrilo
The Macaulay2 package SumsOfSquares decomposes polynomials as sums of squares. It is based on methods to rationalize sum-of-squares decompositions due to Parrilo and Peyrl. The pac…
The Geometry of SDP-Exactness in Quadratic Optimization
Diego Cifuentes, Corey Harris, Bernd Sturmfels
Consider the problem of minimizing a quadratic objective subject to quadratic equations. We study the semialgebraic region of objective functions for which this problem is solved b…
On the local stability of semidefinite relaxations
Diego Cifuentes, Sameer Agarwal, Pablo A. Parrilo +1
We consider a parametric family of quadratically constrained quadratic programs (QCQP) and their associated semidefinite programming (SDP) relaxations. Given a nominal value of the…
Sampling algebraic varieties for sum of squares programs
Diego Cifuentes, Pablo A. Parrilo
We study sum of squares (SOS) relaxations to optimize polynomial functions over a set , where is a complex algebraic variety. We propose a new methodology that, rath…