My research focuses on developing advanced algorithms to solve complex bilevel optimization problems, particularly in image processing and data science. Through this work, I aim to bridge the gap between theoretical mathematics and its practical applications, improving processes like image enhancement and data analysis.
Wim van Ackooij, Diego Morales-Poblete, Pedro Pérez-Aros, David Villacís
Applied Mathematics & Optimization, volume 93, number 2, pages 62, March 2026
In this work, we are concerned with the study of optimization problems featuring so-called probability or chance constraints. Probability constraints measure the level of satisfaction of an underlying random inequality system and ensure that this lev…
pdf articleJuan Carlos De los Reyes, David Villacís
IMA Journal of Applied Mathematics, volume 89, number 1, pages 85-122, September 2023, doi: 10.1093/imamat/hxad024
In this paper, we investigate the use of bilevel optimization for model learning in variational imaging problems. Bilevel learning is an alternative approach to deep learning methods, which leads to fully interpretable models. However, it requires a …
doiJuan Carlos De los Reyes, David Villacís
SIAM Journal on Imaging Sciences, volume 15, number 4, pages 1646-1689, December 2022, doi: 10.1137/21M143412X
We address the problem of optimal scale-dependent parameter learning in total variation image denoising. Such problems are formulated as bilevel optimization instances with total variation denoising problems as lower-level constraints. For the bileve…
pdf doiDavid Villacís
Latin-American Journal of Computing, volume 4, number 3, pages 37-42, November 2017
In this paper we are interested in comparing the performance of some of the most relevant first order non-smooth optimization methods applied to the Rudin, Osher and Fatemi (ROF) Image Denoising Model and a Primal-Dual Chambolle-Pock Image Denoising …
pdf articleJuan Carlos De los Reyes, David Villacís
Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging: Mathematical Imaging and Vision, pages 1–34, February 2022, doi: 10.1007/978-3-030-03009-4_66-1
Optimization techniques have been widely used for image restoration tasks, as many imaging problems may be formulated as minimization ones with the recovered image as the target minimizer. Recently, novel optimization ideas also entered the scene in …
doiDavid Villacís
December 2022
We address the problem of optimal scale-dependent parameter learning in total variation image denoising. Such problems are formulated as bilevel optimization instances with total variation denoising problems as lower-level constraints. For the bileve…
pdf articleDavid Villacís, Pedro Pérez-Aros, Emilio Vilches
June 2025
We study a bilevel optimization framework for hyperparameter learning in variational models, with a focus on sparse regression and classification tasks. In particular, we consider a weighted elastic-net regularizer, where feature-wise regularization …
pdf code articleDavid Villacís, Santeri Kaupinmäki, Samuli Siltanen, Teemu Helenius
February 2022
This document reports the acquisition, structure and properties of a digital photographic dataset collected at the Industrial Mathematics Laboratory of the Department of Mathematics and Statistics of University of Helsinki, Finland. This dataset is d…
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