Department of Mathematics
NC State University
SAS Hall 4125
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 M.Sc. in Applied Mathematics at Universidad de Chile in 2022, under the guidance of Professor Héctor Ramírez. Previously, I worked as an Undergraduate Research Assistant at NIC Chile Research Labs, where I studied Internet Quality of Service (QoS) through stochastic and optimization models.
My research interests lie in nonlinear analysis and optimization, with a focus on convex optimization, stochastic optimization, and optimal control. I am particularly interested in the interplay between randomness and deterministic optimization methods.
Publications
- J. I. Madariaga, An abstract stochastic Haugazeau method for best approximation. [arXiv]
- P. L. Combettes and J. I. Madariaga, Asymptotic analysis of an abstract stochastic scheme for solving monotone inclusions. [arXiv]
- P. L. Combettes and J. I. Madariaga, A geometric framework for stochastic iterations. [arXiv]
- P. L. Combettes and J. I. Madariaga, Almost-surely convergent randomly activated monotone operator splitting methods, SIAM Journal on Imaging Sciences, vol. 18, no. 4, pp. 2177–2205, October 2025. [pdf]
- P. L. Combettes and J. I. Madariaga, Stochastic block-iterative parallel subgradient projections method with super relaxations, Proceedings of EUSIPCO 2025, pp. 2757–2761. Palermo, Italy, September 7–12, 2025. [pdf]
- 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, February 2025. [pdf]
- P. L. Combettes and J. I. Madariaga, Randomly activated proximal methods for nonsmooth convex minimization, Proceedings of EUSIPCO 2024, pp. 2642–2646. Lyon, France, August 26–30, 2024.
- 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 MMSys 2021, pp. 274–280, September 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, February 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, January 2021. [pdf]
- 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 ACM EPIQ 2020, pp. 35–41, August 2020. [pdf]
Teaching
| Calculus I | TA · Fall 2025 |
| Calculus II | TA · Fall 2024; Spring 2025 |
| Calculus for Life and Management Sciences A | TA · Spring 2024; Spring 2026 |
| Modeling and Optimization | TA · Fall 2022 |
| Nonlinear Optimization | TA · Fall 2021 |
| Stochastic Models in Engineering Systems | TA · Spring 2020 |
| Optimal Control: Theory and Laboratory | TA · Spring 2020, 2021, 2022 |
| Mathematical Optimization | TA · Fall 2020 |
| Measure Theory | TA · Spring 2019 |
| Advanced Calculus | TA · Spring 2018 |
| Linear Algebra | TA · Spring 2017 |