Minimum probability of error for asynchronous Gaussian multiple-access channels
IEEE Transactions on Information Theory
Derivatives and perturbations of eigenvectors
SIAM Journal on Numerical Analysis
Laplacian eigenvalues and the maximum cut problem
Mathematical Programming: Series A and B
Convex relaxations of (0, 1)-quadratric programming
Mathematics of Operations Research
On the Rank of Extreme Matrices in Semidefinite Programs and the Multiplicity of Optimal Eigenvalues
Mathematics of Operations Research
Lectures on modern convex optimization: analysis, algorithms, and engineering applications
Lectures on modern convex optimization: analysis, algorithms, and engineering applications
Computers and Intractability; A Guide to the Theory of NP-Completeness
Computers and Intractability; A Guide to the Theory of NP-Completeness
A Spectral Bundle Method for Semidefinite Programming
SIAM Journal on Optimization
Semidefinite programming for discrete optimization and matrix completion problems
Discrete Applied Mathematics
Binary Partitioning, Perceptual Grouping, and Restoration with Semidefinite Programming
IEEE Transactions on Pattern Analysis and Machine Intelligence
Convex Optimization
Semidefinite relaxation based multiuser detection for M-ary PSK multiuser systems
IEEE Transactions on Signal Processing - Part I
Multiuser detection in CDMA - a comparison of relaxations, exact, and heuristic search methods
IEEE Transactions on Wireless Communications
Designing structured tight frames via an alternating projection method
IEEE Transactions on Information Theory
The application of semidefinite programming for detection in CDMA
IEEE Journal on Selected Areas in Communications
| Hi-index | 0.08 |
The goal of this paper is to survey the properties of the eigenvalue relaxation for least squares binary problems. This relaxation is a convex program which is obtained as the Lagrangian dual of the original problem with an implicit compact constraint and as such, is a convex problem with polynomial time complexity. Moreover, as a main practical advantage of this relaxation over the standard semi-definite programming approach, several efficient bundle methods are available for this problem allowing to address problems of very large dimension. The necessary tools from convex analysis are recalled and shown at work for handling the problem of exactness of this relaxation. Two applications are described. The first one is the problem of binary image reconstruction and the second is the problem of multiuser detection in CDMA systems.