Research Fields

Variational Analysis and Dynamical Systems

I study nonsmooth dynamical systems, induced by descent dynamics, sweeping processes and other variational dynamics. I’m also interested in nonsmooth first-order calculus in the convex and nonconvex setting.

Differential geometry and metric analysis in Optimization

I study the metric and differential structure of mathematical objects in the context of variational analysis, such that the metric projection, manifolds in Hilbert spaces, o-minimal structures, metric slopes, among others.

Bilevel Optimization and Game Theory

I’m interested in optimization and equilibrium problems in several settings, such as quasiconvex equilibrium problems, nonsmooth optimization, variational formulations, bilevel optimization and Multi-Leader-Follower games, both in the deterministic and stochastic setting. I study both, theoretical aspects and algorithms.

Applications of Optimization and Learning

I am interested in high impact problems where optimization, game theory and learning are involved. I study applications of these theories, such that sharing economies, cryptocurrencies, design of exchange networks and opinions in social networks.
Problems in renewable energy, and management of natural resources have been one of my research lines in the recent years. I am also interested in problems of Operations research, logistic and economics in general.

Preprints

• Idle wage as a tool to regulate the relationship between ride-hailing platforms and drivers.
  A. Fielbaum, D. Salas, R. Zhang, F. Castro.
  arXiv:2408.13421
• Cardinality Constraints in Single-Leader-Multi-Follower games.
  D. Aussel, D. Lasluisa and D. Salas.
  arXiv:2403.19074
• Reducing the Large Set Threshold for the Basu-Oertel Conjecture.
  A. Cristi and D. Salas.
  arXiv:2411.11864
• Mean-field Concentration of Opinion Dynamics in Random Graphs.
  J. Gutiérrez-Ramírez, D. Salas and V. Verdugo.
  arXiv:2412.03207

Accepted/In Press

• Calificación Basada en Competencias: Adaptaciones Docentes en un Curso Transversal de Ingeniería Civil en la Universidad Estatal de O'Higgins
  G. Liberona, D. Salas.
  Conference: XIII Congreso Latinoamericano sobre Abandono en Educación Superior (CLABES 2024).
  October 23th - October 25th, 2024. Heredia, Costa Rica.
  Best paper Award: Mención de Calidad on the track Prácticas curriculares para la promoción de la permanencia o reducción del abandono.

Published Articles

2024

• Metric compatibility and determination in complete metric spaces.
  A. Daniilidis, T. M. Le and D. Salas.
  Mathematische Zeitschrift, Vol. 308, article number 62, 2024.
  DOI: 10.1007/s00209-024-03609-2
• Descent modulus and applications.
  A. Daniilidis, L. Miclo and D. Salas.
  Journal of Functional Analysis, Vol. 287, nº 11, pp. 110626, 2024.
  DOI: 10.1016/j.jfa.2024.110626
• Steepest geometric descent for regularized quasiconvex functions.
  A. Daniilidis and D. Salas.
  Set-Valued and Variational Analysis, Vol. 32, article 28, 2024.
  DOI: 10.1007/s11228-024-00731-5
• A slope generalization of Attouch theorem.
  A. Daniilidis, D. Salas and S. Tapia-García.
  Mathematical Programming - Series A, pp. 1-30, 2024.
  DOI: 10.1007/s10107-024-02108-w
• Exploiting the polyhedral geometry of stochastic linear bilevel programming.
  G. Muñoz, D. Salas and A. Svensson.
  Mathematical Programming - Series B, pp. 1-36, 2024.
  DOI: 10.1007/s10107-024-02097-w - Acepted version: arXiv:2211.02268
  
• Multidimensional analysis for the techno-economic study of the CSP plant.
  D. Lasluisa, D. Salas, N. Mazet and D. Aussel.
  Journal of Energy Storage, Vol. 86, pp. 110732, 2024.
  DOI: 10.1016/j.est.2024.110732
• The value of Shared Information for allocation of drivers in ride-hailing: a proof-of-concept study.
  G. Liberona, D. Salas and L. von Niederhäusern.
  Computational Management Science, Vol. 21, 4, 2024.
  DOI: 10.1007/s10287-023-00487-7 - Accepted version: arXiv:2201.00061

2023

• Robustness in optimal design of Eco-Industrial Parks under the lens of two-stage stochastic optimization.
  G. Liberona, A. Di Pretoro, S. Negny, L. Montastruc and D. Salas.
  Computers & Chemical Engineering,Vol. 179, pp. 108399, 2023.
  DOI: 10.1016/j.compchemeng.2023.108399
• Existence of solutions for deterministic bilevel games under a general Bayesian approach.
  D. Salas and A. Svensson.
  SIAM Journal on Optimization, Vol. 33, no 3, pp. 2311--2340, 2023.
  DOI: 10.1137/21M1442164 - Accepted version: arXiv:2010.05368v5
• Exploiting the polyhedral geometry of stochastic linear bilevel programming
  G. Muñoz, D. Salas and A. Svensson.
  In: Del Pia, A., Kaibel, V. (eds) Integer Programming and Combinatorial Optimization. IPCO 2023. Lecture Notes in Computer Science, Vol. 13904, pp 363-377, 2023.
  Conference: The 24th Conference on Integer Programming and Combinatorial Optimization (IPCO 2023).
  DOI: 10.1007/978-3-031-32726-1_26 - Full-length pre-print: arXiv:2211.02268
  
• Optimal design of exchange water networks with control inputs in Eco-Industrial Parks.
  D. Aussel, K. Cao Van and D. Salas.
  Energy Economics, Vol. 120, pp. 106480, 2023.
  DOI: 10.1016/j.eneco.2022.106480 - Accepted version: arXiv:2204.09863

2022

• A determination theorem in terms of the metric slope.
  A. Daniilidis and D. Salas.
  Proceedings of the American Mathematical Society, Vol. 150, no 10, pp. 4325--4333, 2022.
  DOI: 10.1090/proc/15958 - Accepted version: arXiv:2109.13721

2021

• Existence results for Generalized Nash Equilibrium Problems under continuity-like properties of sublevel sets.
  D. Aussel, K. Cao Van and D. Salas.
  SIAM Journal of Optimization, Vol. 31, no 4, pp. 2784--2806, 2021.
  DOI:10.1137/20M1353629
• Innovative Application of Model-Based Predictive Control for Low-Voltage Power Distribution Grids with Significant Distributed Generation.
  N. Dkhili, D. Salas, J. Eynard, S. Thil and S. Grieu.
  Energies, Vol. 14, no 6, 2021.
  DOI:10.3390/en14061773
• Quantitative characterizations of nonconvex bodies with smooth boundaries in Hilbert spaces via the metric projection.
  D. Salas and L. Thibault.
  Journal of Mathematical Analysis and Applications, Vol. 494, nº 2, 2021.
  DOI:10.1016/j.jmaa.2020.124588
• Determination of convex functions via subgradients of minimal norm.
  P. Pérez-Aros, D. Salas and E. Vilches.
  Mathematical Programming - Series A, Vol. 190, no 1, pp. 561--583, 2021.
  DOI:10.1007/s10107-020-01550-w

2020

• Optimal design of exchange networks with blind inputs and its application to Eco-industrial parks.
  D. Salas, K. Cao Van, D. Aussel and L. Montastruc.
  Computers & Chemical Engineering, Vol. 143, 2020.
  DOI:10.1016/j.compchemeng.2020.107053
• On formulae for the Ioffe geometric subdifferential of supremum function.
  P. Pérez-Aros, D. Salas and E. Vilches.
  Journal of Convex Analisis, Vol. 27, nº2, pp. 487--508, 2020.
  www.heldermann.de/JCA/JCA27/JCA272/jca27026.htm
• An Application of Model-based Predictive Control for Renewables-intensive Power Distribution Grids
  N. Dkhili, D. Salas, J. Eynard, S. Thil and S. Grieu.
  IFAC-PapersOnLine Vol. 53, no2, pp. 13262--13268, 2020.
  Conference: 21st IFAC-V World Congress
  DOI: 10.1016/j.ifacol.2020.12.155

2019

• Existence results for solutions of quasi-variational inequalities over product sets with quasi-monotone operators.
  D. Aussel, K. Cao Van and D. Salas.
  SIAM Journal on Optimization, Vol. 29, nº 2, pp. 1558--1577, 2019.
  DOI:10.1137/18M1191270
• On characterizations of submanifolds via smoothness of the distance function in Hilbert spaces.
  D. Salas and L. Thibault.
  Journal of Optimization Theory and Applications, Vol. 189, nº1, pp. 189--210, 2019.
  DOI:10.1007/s10957-019-01473-3
• On Smoothness of solutions to projected differential equations.
  D. Salas, L. Thibault and E. Vilches.
  Discrete and Continuous Dynamical Systems - Series A, Vol. 39, nº4, pp. 2255--2283, 2019.
  DOI:10.3934/dcds.2019095
• The value of thermo-chemical storage for CSP: Relevance of peak production strategy on both dimensional and operational optimization.
  E. Tapachès, D. Salas, M. Pierre-Muzet, S. Mauran, D. Aussel and M. Mazet.
  Energy Conversion and Management, Vol. 198, 2019.
  DOI:10.1016/j.enconman.2018.11.082

2018

• Pre-scenarios as economic evaluation technique for thermo-chemical storage in solar plants.
  D. Salas, E. Tapachès, M. Mazet and D. Aussel.
  Energy Conversion and Management, Vol. 174, pp. 932--954, 2018.
  DOI:10.1016/j.enconman.2018.08.079
• Smoothness of the Metric Projection onto Nonconvex Bodies in Hilbert Spaces.
  R. Correa, D. Salas and L. Thibault.
  Journal of Mathematical Analysis and Applications, Vol. 457, nº 2, pp. 1307--1332, 2018.
  DOI:10.1016/j.jmaa.2016.08.064
• Convex smooth-like properties and Faces Radon-Nikodỳm property in Banach spaces.
  D. Salas.
  Studia Mathematica, Vol. 240, nº 3, pp. 231--253, 2018.
  DOI:10.4064/sm8440-3-2017

2016

• Extended Seminorms and Extended Topological Vector Spaces.
  D. Salas and S. Tapia-García.
  Topology and its Applications, Vol. 210, pp. 317--354, 2016.
  DOI:10.1016/j.topol.2016.08.001
• Integration of nonconvex epi-pointed functions in locally convex spaces
  R. Correa, A. Hantoute and D. Salas.
  Journal of Convex Analysis, Vol. 23, nº 2, pp. 511--530, 2016.
  www.heldermann.de/JCA/JCA23/JCA232/jca23019.htm

PhD. Thesis