Research Fields

Variational Analisis 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 in Variational Analysis

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

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

• Descent modulus and applications
  A. Daniilidis, L. Miclo, D. Salas
  arXiv:2211.118198
• Linear bilevel programming with uncertain lower-level costs.
  G. Muñoz, D. Salas and A. Svensson.
  arXiv:2211.02268
  Download first arXiv version 04-11-2022
• The value of shared information in ridesharing problems: a stochastic Stackelberg game approach.
  G. Liberona, L. von Niederhäusern and D. Salas.
  arXiv:2201.00061
• Existence of solutions for deterministic bilevel games under a general Bayesian approach.
  D. Salas and A. Svensson.
  arXiv:2010.05368v4
• The Convergence Rates of Blockchain Mining Games: A Markovian Approach.
  A. Jofré, A. Pardo, D. Salas, V. Verdugo and J. Verschae.
  arXiv:2107.08077

Published Articles

2023

• Optimal design of exchange water networks with control inputs in Eco-Industrial Parks.
  D. Aussel, K. Cao Van and D. Salas.
  Energy Economics, In Press - available Online, 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, no10, 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, no4, 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