The molecule problem is that of determining the relative locations of a set of objects in Euclidean space relying only upon a sparse set of pairwise distance measurements. This NP{hard problem has applications in the determination of molecular conformation. The molecule problem can be naturally expressed as a continuous, global optimization problem, but it also has a rich combinatorial structur...

a method based on electrical capacitance tomography (ect) and an improved least squares support vector machine (ls-svm) is proposed for void fraction measurement of oil-gas two-phase flow. in the modeling stage, to solve the two problems in ls-svm, pruning skills are employed to make ls-svm sparse and robust; then the real-coded genetic algorithm is introduced to solve the difficult problem of ...

The purpose of this paper is to generalize a result byDonoho, Huo, Elad and Bruckstein on sparse representations of signals/images in a union of two orthonormal bases. We consider general (redundant) dictionaries in finite dimension, and derive sufficient conditions on a signal/image for having a unique sparse representation in such a dictionary. In particular, it is proved that the result of D...

A problem of great interest in optimization is to minimize a sum of two closed, proper, and convex functions where one is smooth and the other has a computationally inexpensive proximal operator. In this paper we analyze a family of Inertial Forward-Backward Splitting (I-FBS) algorithms for solving this problem. We first apply a global Lyapunov analysis to I-FBS and prove weak convergence of th...

In this paper, we propose an optimization selection methodology for the ubiquitous sparse matrix-vector multiplication (SpMV) kernel. We propose two models that attempt to identify the major performance bottleneck of the kernel for every instance of the problem and then select an appropriate optimization to tackle it. Our first model requires online profiling of the input matrix in order to det...

We propose a general formulation of nonconvex and nonsmooth sparse optimization problems with convex set constraint, which can take into account most existing types sparsity-inducing terms, bringing strong applicability to wide range applications. design algorithmic framework iteratively reweighted algorithms for solving the proposed problems, solves sequence weighted regularization adaptively ...