Now showing items 21-30 of 67
Group Sparse Optimization by Alternating Direction Method
This paper proposes efficient algorithms for group sparse optimization with mixed L21-regularization, which arises from the reconstruction of group sparse signals in compressive sensing, and the group Lasso problem in ...
A Compressive Sensing and Unmixing Scheme for Hyperspectral Data Processing
Hyperspectral data processing typically demands enormous computational resources in terms of storage, computation and I/O throughputs, especially when real-time processing is desired. In this paper, we investigate a ...
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.
Convergence of a Class of Stationary Iterative Methods for Saddle Point Problems
A unified convergence result is derived for an entire class of stationary iterative methods for solving equality constrained quadratic programs or saddle point problems. This class is constructed from essentially all ...
Computing a Celis-Dennis Tapia Trust Region Step for Equality Constrained Optimization
We study an approach for minimizing a convex quadratic function subject to two quadratic constraints. This problem stems from computing a trust region step for an SQP algorithm proposed by Celis, Dennis and Tapia (1984) ...
Interior-Point Algorithms for Semidefinite Programming Based on A Nonlinear Programming Formulation
Recently, the authors of this paper introduced a nonlinear transformation to convert the positive definiteness constraint on an n × n matrix function of a certain form into the positivity constraint on n scalar variables ...
Solving Semidefinite Programs via Nonlinear Programming, Part II: Interior Point Methods for a Subclass of SDPs
In Part I of this series of papers, we have introduced transformations which convert a large class of linear and nonlinear semidefinite programs (SDPs) into nonlinear optimization problems over "orthants" of the form ...
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 (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 ...