Kimon Fountoulakis Local graph clustering methods aim to identify well-connected clusters around a given “seed set” of reference nodes. The main focus of prior theoretical work has been on worst-case running time properties or on implicit statistical regularization; and the focus of prior empirical work has been to identify structure in large social and information networks. Here, … Read more
We present a novel randomized block coordinate descent method for the minimization of a convex composite objective function. The method uses (approximate) partial second-order (curvature) information, so that the algorithm performance is more robust when applied to highly nonseparable or ill conditioned problems. We call the method Flexible Coordinate Descent (FCD). At each iteration of … Read more
We study the performance of first- and second-order optimization methods for l1-regularized sparse least-squares problems as the conditioning and the dimensions of the problem increase up to one trillion. A rigorously defined generator is presented which allows control of the dimensions, the conditioning and the sparsity of the problem. The generator has very low memory … Read more
In this paper we are concerned with the solution of Compressed Sensing (CS) problems where the signals to be recovered are sparse in coherent and redundant dictionaries. We extend a primal-dual Newton Conjugate Gradients (pdNCG) method for CS problems. We provide an inexpensive and provably effective preconditioning technique for linear systems using pdNCG. Numerical results … Read more
In this paper we present a novel randomized block coordinate descent method for the minimization of a convex composite objective function. The method uses (approximate) partial second-order (curvature) information, so that the algorithm performance is more robust when applied to highly nonseparable or ill conditioned problems. We call the method Robust Coordinate Descent (RCD). At … Read more
In this paper we are interested in the solution of Compressed Sensing (CS) problems where the signals to be recovered are sparse in coherent and redundant dictionaries. CS problems of this type are convex with non-smooth and non-separable regularization term, therefore a specialized solver is required. We propose a primal-dual Newton Conjugate Gradients (pdNCG) method. … Read more
In this paper a robust second-order method is developed for the solution of strongly convex l1-regularized problems. The main aim is to make the proposed method as inexpensive as possible, while even difficult problems can be efficiently solved. The proposed method is a primal-dual Newton Conjugate Gradients (pdNCG) method. Convergence properties of pdNCG are studied … Read more
We consider a class of optimization problems for sparse signal reconstruction which arise in the field of Compressed Sensing (CS). A plethora of approaches and solvers exist for such problems, for example GPSR, FPC AS, SPGL1, NestA, l1 ls, PDCO to mention a few. CS applications lead to very well conditioned optimization problems and therefore … Read more