About
I am a Ph.D. candidate in the Department of Mathematics at NC State University, advised by Professor Patrick L. Combettes. I completed my MSc in Applied Mathematics at the Universidad de Chile in 2022, under the guidance of Professor Héctor Ramírez. I previously worked as an Undergraduate Research Assistant at NIC Chile Research Labs, where I focused on studying Internet Quality of Service (QoS) through stochastic and optimization models.
My research interests encompass nonlinear analysis and optimization, with a focus on convex optimization, stochastic optimization, and optimal control. Specifically, I am interested in the interplay between randomness and deterministic optimization methods.
Publications
Preprints
- P. L. Combettes and J. I. Madariaga, A geometric framework for stochastic iterations. [arXiv]
2025
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P. L. Combettes and J. I. Madariaga, Almost-surely convergent randomly activated monotone operator splitting methods, SIAM Journal on Imaging Sciences, to appear. [pdf]
- P. L. Combettes and J. I. Madariaga, Stochastic block-iterative parallel subgradient projections method with super relaxations, Proceedings of the European Signal Processing Conference, to appear.
- J. I. Madariaga and H. Ramírez, Facial approach for constructing stationary points for mathematical programs with cone complementarity constraints, Journal of Optimization Theory and Applications, vol. 204, no. 15, 2025. [pdf]
2024
2021
- D. Madariaga, L. Torrealba, J. I. Madariaga, J. Bustos-Jiménez, and B. Bustos, PePa Ping Dataset: Comprehensive Contextualization of Periodic Passive Ping in Wireless Networks ACM Multimedia Systems Conference (MMSys ‘21), pp. 274-280, 2021. [pdf]
- D. Madariaga, J. I. Madariaga, J. Bustos-Jiménez, and B. Bustos, Improving Signal Strength Aggregation for Mobile Crowdsourcing Scenarios, MDPI Sensors, vol. 21, p. 1084, 2021. [pdf]
- D. Madariaga, J. I. Madariaga, M. Panza, J. Bustos-Jiménez, and B. Bustos, Detecting Anomalies at a TLD Name Server Based on DNS Traffic Predictions, IEEE Transactions on Network and Service Management, vol. 18, pp. 1016-1030, 2021. [pdf]
2020
- D. Madariaga, L. Torrealba, J. I. Madariaga, J. Bermúdez, and J. Bustos-Jiménez, Analyzing the Adoption of QUIC From a Mobile Development Perspective, Proceedings of the Workshop on Evolution, Performance, and Interoperability of QUIC (EPIQ ‘20). ACM, pp 35-41, 2020. [pdf]
Teaching
North Carolina State University, Department of Mathematics
- Calculus II (TA) [2024 Fall; 2025 Spring]
- Calculus for Life and Management Sciences A (TA) [2024 Spring]
Universidad de Chile, Faculty of Physical and Mathematical Sciences
- Modeling and Optimization (TA) [2022 Fall]
- Nonlinear Optimization (TA) [2021 Fall]
- Stochastic Models in Engineering Systems (TA) [2020 Spring]
- Optimal Control: Theory and Laboratory (TA) [2020 Spring; 2021 Spring; 2022 Spring]
- Mathematical Optimization (TA) [2020 Fall]
- Measure Theory (TA) [2019 Spring]
- Advanced Calculus (TA) [2018 Spring]
- Linear Algebra (TA) [2017 Spring]
Theses
- Condiciones de Optimalidad para la Programación Cónica con Restricciones de Complementariedad, Master’s Thesis, Universidad de Chile, 2022. [pdf (in Spanish)]