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About
I am a Ph.D. student in the Department of Mathematics at NC State University, advised by Professor Patrick L. Combettes. I completed my MSc in Applied Mathematics at the University of 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 include nonlinear analysis and optimization, focusing 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, Almost-surely convergent randomly activated monotone operator splitting methods. [arXiv]
2025
- 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
- P. L. Combettes and J. I. Madariaga, Randomly activated proximal methods for nonsmooth convex minimization, Proceedings of the European Signal Processing Conference, pp. 2642–2646. Lyon, France, August 26–30, 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]
University of 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)]