CME 510: Linear Algebra and Optimization Seminar

This seminar series highlights recent developments in numerical linear algebra and numerical optimization. The goal is to bring together scientists from different theoretical and application areas to solve complex scientific computing problems. Presenters include academic researchers and industrial R&D staff.

Wednesday Feb 26, 2025    4:30--5:30pm, Building 300-303  (behind the church toward the Clock Tower)   

Dr Alexis Montoison    Argonne National Laboratory

Recovering sparse DFT on missing signals via an interior method    for optimization (MadNLP) on GPU We propose a method to recover the sparse discrete Fourier transform (DFT) of a signal that is both noisy and potentially incomplete, with missing values.  A least-squares problem based on the inverse discrete Fourier transform (IDFT) with an l1-penalty term is reformulated to be solvable using a primal-dual interior point method (IPM).  The problem is equivalent to Basis Pursuit Denoising (BPDN).  The original BPDN solver PDCO uses an IPM with subproblems handled by the Krylov solver LSMR.  Here our IPM MadNLP employs PCG with a tailored preconditioner. We establish new asymptotic bounds on the condition number of the preconditioned matrices within MadNLP. We present numerical results for a Julia implementation on real problems from diffuse scattering experiments, and large artificial problems.  Our code relies on the software MadNLP.jl, Krylov.jl, and cuFFT, all optimized for GPU parallelism to ensure scalability on problems involving hundreds of millions of variables. 

Speaker Bio: Alexis Montoison is a postdoctoral researcher in the Mathematics and Computer Science division at Argonne National Laboratory.  He focuses on developing high-performance algorithms for sparse linear algebra, continuous optimization, and automatic differentiation, with an emphasis on multi-architecture compatibility across CPUs and GPUs. He received his PhD in applied mathematics from Polytechnique Montréal under the supervision of Dominique Orban, where he was awarded GERAD's Best Thesis Award for his work "Krylov Methods for Linear Algebra and Polymorphic Implementation".  Alexis has developed several novel iterative solvers and techniques for large-scale linear systems, including MinAres, an iterative solver for symmetric linear systems. He is the principal developer of both Krylov.jl and libHSL, a collection of widely used libraries of sparse-matrix algorithms.  His academic achievements have been recognized through multiple honors, including travel awards from SIAM and scholarships from the Arbour Foundation, FRQNT, and IVADO, underscoring his dedication to advancing both theoretical and numerical approaches to numerical linear algebra and optimization.