Now showing items 11-20 of 67
A Simple Proof for Recoverability of L1-Minimization (II): the Nonnegativity Case
When using L1 minimization to recover a sparse, nonnegative solution to a under-determined linear system of equations, what is the highest sparsity level at which recovery can still be guaranteed? Recently, Donoho and ...
Practical Compressive Sensing with Toeplitz and Circulant Matrices
Compressive sensing encodes a signal into a relatively small number of incoherent linear measurements. In theory, the optimal incoherence is achieved by completely random measurement matrices. However, such matrices are ...
An Alternating Direction Algorithm for Nonnegative Matrix Factorization
We extend the classic alternating direction method for convex optimization to solving the non-convex, non- negative matrix factorization problem and conduct several carefully designed numerical experiments to compare the ...
Comparison of Two Sets of First-order Conditions as Bases of Interior-Point Newton Methods for Optimization with Simple Bounds
In this paper, we compare the behavior of two Newton interior-point methods derived from two different first-order necessary conditions for the same nonlinear optimization problem with simple bounds. One set of conditions ...
User's Guide for LMaFit: Low-rank Matrix Fitting
This User's Guide describes the functionality and basic usage of the Matlab package LMaFit for low-rank matrix optimization. It also briefly explains the formulations and algorithms used.
Accelerating the Lee-Seung Algorithm for Nonnegative Matrix Factorization
Approximate nonnegative matrix factorization is an emerging technique with a wide spectrum of potential applications in data analysis. Currently, the most-used algorithms for this problem are those proposed by Lee and ...
Solution-Recovery in L1-norm for Non-square Linear Systems: Deterministic Conditions and Open Questions
Consider an over-determined linear system A'x = b and an under-determined linear system By = c. Given b = A'x* + h, under what conditions x* will minimize the residual A'x - b in L1-norm? On the other hand, given c = Bh, ...
A Simple Proof for Recoverability of L1-Minimization: Go Over or Under?
It is well-known by now that L1 minimization can help recover sparse solutions to under-determined linear equations or sparsely corrupted solutions to over-determined equations, and the two problems are equivalent under ...
On Theory of Compressive Sensing via L_1-Minimization: Simple Derivations and Extensions
Compressive (or compressed) sensing (CS) is an emerging methodology in computational signal processing that has recently attracted intensive research activities. At present, the basic CS theory includes recoverability and ...
A Computational Study of a Gradient-Based Log-Barrier Algorithm for a Class of Large-Scale SDPs
The authors of this paper recently introduced a transformation that converts a class of semidefinite programs (SDPs) into nonlinear optimization problems free of matrix-valued constraints and variables. This transformation ...