joint work with Panos Parpas, Ivan Stoianov
We focus on inverse problems for physical systems subject to a set of non-linear equations and formulate a generic sequential convex optimization solution method. The proposed algorithm is implemented for fault estimation in water supply networks. Previous literature has solved this combinatorial problem using evolutionary approaches. We show that the considered problem can be approximated by a non-linear inverse problem with L1 regularization and solved using sequential convex optimization. The developed method is tested using a large operational water network as case study.
joint work with Panos Parpas, Chin Pang Ho
Building upon multigrid methods, a framework of multilevel optimization methods was developed to solve structured optimization problems, including problems in optimal control, image processing, etc. In this talk, we give a broader view of the multilevel framework and establish some connections between multilevel algorithms and the other approaches. By studying a case study of the so-called Newton-type multilevel model, we take the first step to show how the structure of optimization problems could improve the convergence of multilevel algorithms.
joint work with Nicolas Gillis
Non-negativity constraint is ubiquitous. A family of non-negativity constrained problems (NCP) are the non-negative least squares (NNLS), the non-negative matrix factorization (NMF) and the non-negative tensor factorization (NTF). The goal of these NCP problems in general is to fit an given object (vector, matrix, or tensor) by solving an optimization problem with non-negativity constraints. Various algorithms are proposed to solve the NCP. In this talk, we introduce an general extrapolation-based acceleration scheme that that can significantly accelerate the algorithm for NNLS, NMF and NTF.