About

I am currently a Ph.D. student in the Department of Mathematics at NC State University, under the mentorship of Professor Patrick L. Combettes. In 2022, I successfully completed my MSc degree in Mathematics Engineering at the University of Chile, where I received valuable guidance from Professor Héctor Ramírez C. Prior to pursuing my graduate studies, I gained practical experience as an Undergraduate Research Assistant at NIC Chile Research Labs, where my work was centered around the implementation of Stochastic and Optimization Models in the context of Internet Quality of Service (QoS) research. My research interests are optimization, nonlinear analysis, convex optimization, and variational analysis.

Contact

SAS Hall 4125; jimadari [at] ncsu.edu

Publications

• P. L. Combettes and J. I. Madariaga, Randomly activated proximal methods for nonsmooth convex minimization. [arXiv]
• 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]
• 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 for Life and Management Sciences A (TA) [2024 Spring]

University of Chile, Faculty of Physical and Mathematical Sciences

• Linear Algebra (TA) [2017 Spring]
• Advanced Calculus (TA) [2018 Spring]
• Measure Theory (TA) [2019 Spring]
• Mathematical Optimization (TA) [2020 Fall]
• Optimal Control: Theory and Laboratory (TA) [2020 Spring; 2021 Spring; 2022 Spring]
• Stochastic Models in Engineering Systems (TA) [2020 Spring]
• Nonlinear Optimization (TA) [2021 Fall]
• Modeling and Optimization (TA) [2022 Fall]

Theses

Master in Engineering Sciences, minor Applied Mathematics

On Optimality Conditions for Nonlinear Conic Programming with Complementarity Constraints, 2022. [pdf]

Abstract: The main purpose of this thesis is to study the conic generalization of MPCC problems, called Conic Mathematical Programs with Complementarity Constraints (CMPCC). Due to the difficulty in qualifying the points in these problems (e.g., the Robinson constraint qualification does not hold at any feasible point), it is necessary to formulate new concepts and definitions of stationary points with which dual optimality conditions can be written. Building on existing results for MPCC and recently reported results for the cone of semidefinite matrices and the second-order cone, general definitions are presented, along with new notions of facial points. Finally, the relationship between all of them is studied. On the other hand, using one of Chi Ngoc Do’s results, the relationship between the tangent cone of the complementarity cone with the subdifferential of the second subderivative of the indicator function is studied. Additionally, to the author’s knowledge, the second parabolic subderivative is defined for the first time. Thus, from a new version of Do’s theorem, the relationship between the second order tangent set of the complementarity cone and the subdifferential of the second parabolic subderivative is studied. Finally, a new facial constraint qualification is presented with which primal optimality conditions can be written.