Confirmed minicourses:
"Applied Optimal Transport: Theory, Surrogates, and Data Applications", by ROCIO DIAZ MARTIN (Florida State University, USA)
Abstract: Optimal transport provides a geometric framework for comparing probability distributions and has become an important tool in analysis, data science, signal processing, and machine learning. This mini-course will introduce the main theoretical formulations of optimal transport, discuss computationally efficient alternatives to the classical Wasserstein distance, and illustrate their use through numerical examples and data applications.
Our first and foundational goal will be to understand the optimal transport problem and the two main tools it provides: a distance between probability distributions and an assignment of mass between them. We will then focus on methods designed to reduce the computational cost of optimal transport, particularly in high-dimensional and large-scale settings. Finally, we will illustrate how these ideas can be used in practice. The course will combine mathematical foundations with computational demonstrations and will introduce participants to the standard literature and widely used Python libraries.
Outline:
Class 1: The Four Faces ot Optimal Transport: - We will introduce four classical formulations of the optimal transport problem: the Monge formulation, the Kantorovich relaxation, the Kantorovich dual problem, and the dynamic formulation of Benamou and Brenier.
Class 2: Surrogates: - Because solving optimal transport problems can be computationally expensive, particularly in high dimensions or for large datasets, we will introduce three approaches that alleviate this difficulty: sliced optimal transport, entropy-regularized optimal transport, and linearized optimal transport.7
Class 3: Applications: - We will close the course with a range of applications and illustrative examples of optimal transport and its surrogates, from signal and image processing, classification, dimensionality reduction, and Wasserstein generative adversarial networks.
"Optimization with JuMP – modeling, solvers, and the ecosystem", by JOAQUIM DIAS GARCIA (Soma Energy | Core dev at JuMP)
Abstract: Mathematical optimization is a core tool of applied mathematics, operations research, and control, but there is a long road between writing a model on paper and solving it reliably at scale. This minicourse is a hands-on introduction to JuMP, the open-source algebraic modeling language embedded in Julia, which lets users express linear, mixed-integer, conic, and nonlinear problems in natural mathematical syntax and solve them with dozens of interchangeable open-source and commercial solvers. Following the full life cycle of an optimization model - from first formulation, through debugging and performance, to the ecosystem where optimization meets machine learning, decision-making under uncertainty and more - the course is example-driven, with short in-class exercises and take-home problems. No prior experience with Julia is assumed; familiarity with basic optimization concepts is helpful.
Outline:
Class 1: Julia and JuMP fundamentals - Essentials of the Julia language and its package manager; building complete models in JuMP: variables, constraints, objectives, solving, and querying solutions and duals; the solver landscape, from open-source solvers to GPU-based methods.
Class 2: From models to software - Structuring larger models: index sets, expressions, parameters, in-place modification and re-solves, and nonlinear programming; debugging models that are wrong (infeasibility, unboundedness, numerical issues) and models that are slow (build vs. solve time, formulation pitfalls).
Class 3: The ecosystem - Packages, AI, Uncertainty and more - Bridging optimization and machine learning (DiffOpt.jl & MathOptAI.jl); multistage stochastic optimization (SDDP.jl); bilevel optimization and pricing (BilevelJuMP.jl); infinite-dimensional optimization (InfiniteOpt.jl); and a guided tour of the wider JuMP ecosystem.
See the list of speakers and poster presenters below, as well as the Book of Abstracts, which contains detailed information about the speakers and their abstracts.
List of speakers, for short and long talks:
Towards Feedback Control of Hyperbolic PDEs via Dynamic Programming and Calibrated Model Reduction,
ALESSANDRO ALLA - Sapienza Università di Roma, Italy.
Convergence Rates for Stochastic Proximal and Projection Estimators,
EMILIO VILCHES – Universidad de O’Higgins, Chile.
Heuristic methodology for linear mathematical programming,
FERNANDA M. PEREIRA - FGV EMAp, Brazil.
Differentiability and Approximation of Probability Functions under Gaussian Mixture Models,
GONZALO CONTADOR - Universidad Técnica Federico Santa María, Chile.
From Nash Games to Vector Equilibrium Problems,
JOHN COTRINA - Universidad del Pacífico, Peru.
On the Structure of Optimal Parameters in Bilevel Learning of Total Variation-Based Inverse Problems,
JUAN CARLOS DE LOS REYES – Escuela Politécnica Nacional & MODEMAT, Ecuador.
Robust topology optimization of continuous structures using the Bernstein approximation,
MIGUEL CARRASCO - Universidad de Los Andes, Chile.
A second-order algorithm for group-sparse optimization,
PEDRO MERINO – Escuela Politécnica Nacional & MODEMAT, Ecuador.
Robust Mean Estimation in High Dimensions: A Statistical Optimization Landscape,
PHILIP THOMPSON – FGV EMAp, Brazil.
Existence and Uniqueness of Optimal Control in Non-Linear Age-Structured Population Dynamics,
RODRIGO MORENO - Universidad Austral, Argentina.
Analysis of a Second-Kind Variational Inequality in Porous Media Flow,
SERGIO GONZÁLEZ-ANDRADE – Escuela Politécnica Nacional & MODEMAT, Ecuador.
A theoretical mathematical model for endogenous growth including the environment,
WILFREDO SOSA - Catholic University of Brasilia, Brazil.
Uniqueness of unbounded viscosity solutions of Hamilton-Jacobi equations with mechanical Hamiltonian in the Wasserstein space,
CRISTOPHER HERMOSILLA - Universidad Técnica Federico Santa María, Chile.
Optimal leveraging of smoothness and strong convexity for the Peaceman–Rachford splitting,
LUIS BRICEÑO ARIAS – Universidad Técnica Federico Santa María, Chile.
Hamilton–Jacobi Equations on Wasserstein Space: an Optimal Transport Approach to the Vanishing Viscosity Limit,
DANIELA TONON – Università di Padova, Italy.
Model Predictive Control for Real-Time Viscosity Regulation in Cementitious Ink Mixing and Pumping for 3D Printing,
DIEGO ALEJANDRO MUÑOZ - Universidad Nacional de Colombia (UNAL), Colombia.
Hamilton-Jacobi equations on networks: the PDE approach for Optimal Control problems on stratified media,
ERWIN TOPP PAREDES - Universidade Federal do Rio de Janeiro, Brazil.
Different approaches to the existence of projected solutions in Banach spaces,
YBOON GARCIA RAMOS - Universidad del Pacífico, Peru.
An asymmetric progressive decoupling algorithm with applications in stochastic variational inequalities,
LISANDRO PARENTE – CONICET & Universidad Nacional de Rosario (UNR), Argentina.
Excess and Hausdorff-type distance for sets via the oriented distance function: theory and applications,
RUBEN LOPEZ - Departamento de Matemática, Universidad de Tarapacá, Arica, Chile.
Numerical approximation of optimal control problems governed by sweeping processes,
JUSTINA GIANATTI – CONICET & Universidad Nacional de Rosario (UNR), Argentina.
A Relative Value iteration framework for SDDP,
BERNARDO FREITAS PAULO DA COSTA – FGV EMAp, Brazil.
Variational Convexity and Proximal-Gradient Methods: Local Convergence and Inexact Extensions,
RAUL TINTAYA - Center of Mathematical Modeling, CMM, Chile.
Gradient extremals, talwegs, valleys, and directional alignment for generic gradient descent,
FRANCISCO JOSÉ SILVA ÁLVAREZ – Université de Limoges, France.
Investment and Operational Planning for electricity markets with massive entry of renewable energy,
ALEJANDRO JOFRÉ - CMM & DIM, Universidad de Chile, Chile.
Rockafellian Perturbations in Finance and Energy Systems: Stability, Relaxation, and Tractable Approximations,
JULIO DERIDE - Universidad Adolfo Ibáñez, Chile.
Industrial Mathematics in Action: Full Waveform Inversion,
JUAN PABLO LUNA - Universidade Federal do Rio de Janeiro, Brazil.
Pontryagin principle for time-optimal problems with almost sure state constraints,
PIERO VISCONTI - University of Klagenfurt, Austria.
On the Stabilisation of Interacting Particle Systems and its Connection to Energy Convexification,
LUCAS MOSCHEN - Imperial College London, United Kingdom.
From simple to general networks: Social Optimum in the common-lines problem,
VICTORIA MARIA ORLANDO - CONICET & Universidad Nacional de Rosario (UNR), Argentina.
Koopman Kalman Filter (KKF): An asymptotically optimal nonlinear filtering algorithm with error bounds and its application to parameter estimation,
HÉCTOR RAMÍREZ - - Universidad de Chile & CMM, Chile.
Variable stepsize splitting methods as relocated fixed-point iterations,
FELIPE ATENAS - Universidad de Chile & CMM, Chile.
Coordinate Descent Methods for Nonseparable Composite Optimization,
FLÁVIA CHOROBURA - Universidade Estadual do Centro-Oeste, Brazil.
From functional and geometric inequalities to quantitative stability of variational problems in optimal transport and convex geometry,
JOÃO MIGUEL MACHADO - Lagrange Mathematics and Computing Research Center, France.
Dynamical Perspectives for Non-Convex Global Optimization,
DANTE KALISE - Imperial College London, United Kingdom.
Basis pursuit by inconsistent alternating projections,
PAULO SILVA - UNICAMP, Brazil.
List of poster presenters:
Hybrid Simulation Optimization Framework for Cyclic CO2 Capture in Fixed-Bed Reactors via Reactive Absorption,
MARIA LAURA RODRÍGUEZ - Instituto de Investigación en Tecnología Química, Argentina.
A Splitting Algorithm for Convex Optimization with Nonlinear Compositions,
SERGIO LÓPEZ RIVERA - Universidad Técnica Federico Santa Maria, Chile.
Evaluation of Advanced Control Strategies: A Comparison between Sequential Predictive Control and Optimized Restrictive Control,
FEDERICO MIRANDA - Universidad Nacional de San Luis, Argentina.
Continuous-time Investment and Operational Planning for Electricity Markets,
MATIAS VERA - Zúrich ETH, Switzerland.
Controlled and delayed exponential stability of the Lotka-Volterra equation,
DAVID CASTILLO-FERNANDEZ - UAM, Mexico.
Cyber risk prevention under risk averse spectral criteria,
MARIANO VAZQUEZ GAETE - Universidad de Chile.
Renewable-Constrained AC Optimal Control via Convex Relaxation,
BRENDA NEQUIZ GUILLEN - UAM, Mexico.
Studies on the Rao–Nakra Sandwich Beam: Well-Posedness, Dynamics, and Controllability,
GEORGE BAUTISTA SANCHEZ - Universidade Federal Fluminense, Brazil.
Mond Weir Duality and Saddle Point Analysis on Riemannian Manifolds for Interval-Valued Optimization Problems,
MAHWASH AFTAB - Aligarh Muslim University, now visiting USP, Brazil.
Second-Order Convergence Analysis of Augmented Lagrangian Methods on Riemannian Manifolds,
HILAL AHMAD BHAT - Universidade de Sao Paulo, Brazil.
Impulsive Dynamical Modeling of COVID-19 Antiviral Therapy: Correcting Drug Accumulation and Preventing Rebound via Phase Plane Analysis,
ALEJO RAMÍREZ - Universidad Nacional del Litoral, Argentina.
Feasibility and full dimension of higher-order Voronoi cells,
MICAELA ARACELI VIRGA - Universidad Nacional de Cuyo, Argentina.
A Mean Field Game Model for Energy Markets,
WENDELL OLIVEIRA - FGV EMAp, Brazil.
Average optimal control of control-affine systems and singular arc,
GABRIEL DE LIMA MONTEIRO - FGV EMAp, Brazil.
Advances in constant-rank type conditions: new connections to MFCQ and local error bounds,
MARIANA DA ROSA - UNICAMP, Brazil.
Deep learning and elicitability for McKean-Vlasov FBSDEs with common noise,
FELIPE ANTUNES - FGV EMAp, Brazil.
Random Gradient-Free Optimization in Infinite Dimensional Spaces,
CAIO PEIXOTO - FGV EMAp, Brazil.
Exact local controllability by trajectories for a Quasi-linear Parabolic PDE with Bilinear-control,
CRISTIAN LOLI - Universidade Federal Fluminense, Brazil.
Multiscale Stochastic Control with Domain Restriction in the Slow Variable,
ANDERSON CALIXTO - Universidade Federal Fluminense, Brazil.
Non-degenerate equilibria for first-order Mean Field Games,
FEDERICO DAMIAN MIEREZ - Universidad Nacional de Rosario, Argentina.
Book of Abstracts: