Related papers: Disentangling Orthogonal Matrices
Solution and analysis of mathematical programming problems may be simplified when these problems are symmetric under appropriate linear transformations. In particular, a knowledge of the symmetries may help reduce the problem dimension, cut…
This paper develops a new storage-optimal algorithm that provably solves generic semidefinite programs (SDPs) in standard form. This method is particularly effective for weakly constrained SDPs. The key idea is to formulate an approximate…
This paper studies the problem of reconstructing binary matrices that are only accessible through few evaluations of their discrete X-rays. Such question is prominently motivated by the demand in material science for developing a tool for…
We study the quadratic $k$-vertex-disjoint paths problem (Q-$k$-VDP), which seeks $k$ vertex-disjoint paths in a directed graph that minimize a nonconvex quadratic objective function. We formulate the problem as a binary quadratic program…
This paper offers a matrix-free first-order numerical method to solve large-scale conic optimization problems. Solving systems of linear equations pose the most computationally challenging part in both first-order and second-order numerical…
Bounding the correlations predicted by quantum theory is an important challenge in quantum information science. Today's leading approach is semidefinite programming relaxations, but existing methods still cannot account for many relevant…
We present a novel deep learning approach to approximate the solution of large, sparse, symmetric, positive-definite linear systems of equations. These systems arise from many problems in applied science, e.g., in numerical methods for…
In this paper we study the problem of recovering a low-rank matrix from linear measurements. Our algorithm, which we call Procrustes Flow, starts from an initial estimate obtained by a thresholding scheme followed by gradient descent on a…
We present semi-decentralized and distributed algorithms, designed via a preconditioned forward-backward operator splitting, for solving large-scale, decomposable semidefinite programs (SDPs). We exploit a chordal aggregate sparsity pattern…
The two-matrix model can be solved by introducing bi-orthogonal polynomials. In the case the potentials in the measure are polynomials, finite sequences of bi-orthogonal polynomials (called "windows") satisfy polynomial ODEs as well as…
We approximate the backward reachable set of discrete-time autonomous polynomial systems using the recently developed occupation measure approach. We formulate the problem as an infinite-dimensional linear programming (LP) problem on…
We investigate the use of linear programming tools for solving semidefinite programming relaxations of quadratically constrained quadratic problems. Classes of valid linear inequalities are presented, including sparse PSD cuts, and…
We consider optimization problems containing nonconvex quadratic functions for which semidefinite programming (SDP) relaxations often yield strong bounds. We investigate linear inequalities that outer approximate the positive semidefinite…
In this work, we consider the low rank decomposition (SDPR) of general convex semidefinite programming problems (SDP) that contain both a positive semidefinite matrix and a nonnegative vector as variables. We develop a rank-support-adaptive…
For verifying the safety of neural networks (NNs), Fazlyab et al. (2019) introduced a semidefinite programming (SDP) approach called DeepSDP. This formulation can be viewed as the dual of the SDP relaxation for a problem formulated as a…
A class of splitting alternating algorithms is proposed for finding the sparse solution of linear systems with concatenated orthogonal matrices. Depending on the number of matrices concatenated, the proposed algorithms are classified into…
In this work we describe an efficient implementation of a hierarchy of algorithms for the decomposition of dense matrices over the field with two elements (GF(2)). Matrix decomposition is an essential building block for solving dense…
We describe several algorithms for matrix completion and matrix approximation when only some of its entries are known. The approximation constraint can be any whose approximated solution is known for the full matrix. For low rank…
Optimal recursive decomposition (or DR-planning) is crucial for analyzing, designing, solving or finding realizations of geometric constraint sytems. While the optimal DR-planning problem is NP-hard even for general 2D bar-joint constraint…
Dual decomposition is a powerful technique for deriving decomposition schemes for convex optimization problems with separable structure. Although the Augmented Lagrangian is computationally more stable than the ordinary Lagrangian, the…