Computational aspects of a three dimensional non-intrusive particle motion tracking system

Development of a technique for non-intrusive particle motion tracking in three dimensions is considered. This technique is based on the principle of magnetic induction. In particular, the determination of the position and onentation of the particle from the information gathered is the pnncipal focus of this thesis. The development of such a system is motivated by the need to understand the flow patterns of granular material. This is of cntical importance in dealing with problems associated with bulk solids flows which occur in almost all industries and in natural geological events. A study of the current diagnostic techniques reveals the limitations in their ability to track the motion of an individual particle in a mass flow of other particles. These techniques fail when the particle must be tracked in three dimensions in a non-intrusive manner. The diagnostic technique we consider results in an unconstrained minimization problem of an overdetennined system of nonlinear equations. The Levenberg-Marquardt algorithm is used to solve such a system to predict the location of the particle. The viability of this technique is established through simulated and actual expenmental results. Practical problems such as the effect of noise are considered. Directions for future work are provided

Optimization with Sparsity-Inducing Penalties

Sparse estimation methods are aimed at using or obtaining parsimonious representations of data or models. They were first dedicated to linear variable selection but numerous extensions have now emerged such as structured sparsity or kernel selection. It turns out that many of the related estimation problems can be cast as convex optimization problems by regularizing the empirical risk with appropriate non-smooth norms. The goal of this paper is to present from a general perspective optimization tools and techniques dedicated to such sparsity-inducing penalties. We cover proximal methods, block-coordinate descent, reweighted $\ell_2$-penalized techniques, working-set and homotopy methods, as well as non-convex formulations and extensions, and provide an extensive set of experiments to compare various algorithms from a computational point of view