We present a new algorithm for nonnegative least-squares (NNLS). Our algorithm extends the unconstrained quadratic optimization algorithm of Barzilai and Borwein (BB) (J. Barzilai and J. M. Borwein; Two-Point Step Size Gradient Methods. IMA J. Numerical Analysis; 1988.) to handle nonnegativity constraints. Our extension diff ers in several basic aspects from other constrained BB variants. The … Read more
We consider the inversion of a linear operator with centered Gaussian white noise by MAP estimation with a Gaussian prior distribution on the solution. The actual estimator is computed approximately by a numerical method. We propose a relation between the stationarity measure of this approximate solution to the mean square error of the exact solution. … Read more
We develop a framework for a class of derivative-free algorithms for the least-squares minimization problem. These algorithms are based on polynomial interpolation models and are designed to take advantages of the problem structure. Under suitable conditions, we establish the global convergence and local quadratic convergence properties of these algorithms. Promising numerical results indicate the algorithm … Read more
The basis pursuit problem seeks a minimum one-norm solution of an underdetermined least-squares problem. Basis pursuit denoise (BPDN) fits the least-squares problem only approximately, and a single parameter determines a curve that traces the optimal trade-off between the least-squares fit and the one-norm of the solution. We prove that this curve is convex and continuously … Read more
This work addresses the problem of regularized linear least squares (RLS) with non-quadratic separable regularization. Despite being frequently deployed in many applications, the RLS problem is often hard to solve using standard iterative methods. In a recent work [10], a new iterative method called Parallel Coordinate Descent (PCD) was devised. We provide herein a convergence … Read more