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• W2184136339 abstract "Author(s): Rabbani, Tarek | Advisor(s): El-Ghaoui, Laurent; Bayen, Alexandre | Abstract: In this thesis, we study two topics related to large-scale sparseestimation and control. In the first topic, we describe a method toeliminate features (variables) in $ell_{1}$-regularized convex optimizationproblems. The elimination of features leads to a potentially substantialreduction in computational effort needed to solve such problems, especiallyfor large values of the penalty parameter. Our method is not heuristic:it only eliminates features that are guaranteed to be absent aftersolving the optimization problem. The feature elimination step iseasy to parallelize and can test each feature for elimination independently.Moreover, the computational effort of our method is negligible comparedto that of solving the convex problem.We study the case of $ell_{1}$-regularized least-squares problem(a.k.a. LASSO) extensively and derive a closed-form sufficient conditionfor eliminating features. The sufficient condition can be evaluatedby few vector-matrix multiplications. For comparison purposes, wepresent a LASSO solver that integrates SAFE with the Coordinate Descentmethod. We call our method CD-SAFE, and we report the number of computationsneeded for solving a LASSO problem using CD-SAFE and using the plainCoordinate Descent method. We observe at least a $100$ fold reductionin computational complexity for dense and sparse data-sets consistingof millions of variables and millions of observations. Some of thesedata-sets can cause memory problems when loaded, or need specializedsolvers. However, with SAFE, we can extend LASSO solvers capabilitiesto treat large-scale problems, previously out of their reach. Thisis possible, because SAFE eliminates variables and thus portions ofour data at the outset, before loading it into our memory.We also show how our method can be extended to general $ell_{1}$-regularizedconvex problems. We present preliminary results for the Sparse SupportVector Machine and Logistic Regression problems.In the second topic of the thesis, we derive a method for open-loopcontrol of open channel flow, based on the Hayami model, a parabolicpartial differential equation resulting from a simplification of theSaint-Venant equations. The open-loop control is represented as infiniteseries using differential flatness, for which convergence is assessed.Numerical simulations show the effectiveness of the approach by applyingthe open-loop controller to irrigation canals modeled by the fullSaint-Venant equations. We experiment with our controller on the Gignac Canal, located northwestof Montpellier, in southern France. The experiments show that it ispossible to achieve a desired water flow at the downstream of a canalusing the Hayami model as an approximation of the real-system. However,our observations of the measured water flow at the upstream controlledgate made us realize some actuator limitations. For example, deadbandin the gate opening and unmodeled disturbances such as friction inthe gate-opening mechanism, only allow us to deliver piece-wise constantcontrol inputs. This fact made us investigate a way to compute a controllerthat respects the actuator limitations. We use the CD-SAFE algorithm,to compute such open-loop control for the upstream water flow. Wecompare the computational effort needed to obtain an open-loop controlwith certain dynamics using the CD-SAFE algorithm and the plain CoordinateDescent algoirthm. We show that with CD-SAFE we are able to obainan open-loop control signal with cheaper computations." @default.
• W2184136339 created "2016-06-24" @default.
• W2184136339 creator A5045356739 @default.
• W2184136339 date "2013-01-01" @default.
• W2184136339 modified "2023-09-27" @default.
• W2184136339 title "Topics in Large-Scale Sparse Estimation and Control" @default.
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