Upcoming talks

• May 13th 2026, 2:00 p.m. - Aula Caminetto - Santa Marta  Justo Puerto (Professor at Universidad de Sevilla) 

Title: Ordered optimization: theory and applications

Abstract: Ordered measures provide a powerful and flexible modeling paradigm, including a wide range of objectives such as fairness indices, risk and robustness criteria, among other aggregation operators. Despite their relevance, their integration into optimization models remains challenging, since ordering operations cannot be decoupled and must be embedded directly into the decision process. In this paper, a unified optimization framework is introduced for the computation and optimization of a broad class of ordered measures within a single algebraic structure. The proposed framework covers linear, quadratic, and nested ordered measures, yielding compact and strengthened mixed integer formulations that generalize many existing models. Structural properties and modeling trade-offs arising from different representations of ordering constraints are discussed. An extensive computational study is conducted to compare the alternative formulations. Finally, the versatility of the proposed framework is illustrated by integrating ordered measures into some representative optimization problems, namely quantile regression, robust scenario aggregation, Traveling Salesman Problem, and Weighted Set Covering Problem. These applications demonstrate how ordered measures can be systematically embedded into complex optimization models without ad hoc reformulations.

• June 15th 2026, 2:00 p.m. Room 012 Centro Didattico Morgagni, Paulo José da Silva e Silva (Associate Professor at Universidade Estadual de Campinas)

Title: Parallel Newton methods for the continuous quadratic knapsack problem: A Jacobi and Gauss-Seidel tale

Abstract: The continuous quadratic knapsack (CQK) problem involves minimizing a diagonal convex quadratic function subject to box constraints and a single linear equality constraint. It has numerous applications in resource allocation, multicommodity flow, machine learning, and classical optimization tasks such as Lagrangian relaxation and quasi-Newton updates. In this work, we revisit the semismooth Newton method introduced by Cominetti, Mascarenhas, and Silva. We demonstrate that the method can be significantly improved in two directions. First, for projections onto the simplex or the l1-ball, it can incorporate Condat's highly effective initial multiplier guess. Second, it can serve as a flexible foundation for CQK algorithms, allowing for different parallel variants tailored to exploit CPU and GPU computational models. These improvements are implemented in the open-source Julia package NewtonCQK.jl. We present extensive numerical tests comparing this implementation with other state-of-the-art solvers, demonstrating its superior efficiency and scalability.e propose an efficient method to generate so-called heatmaps for the maximum coverage facility location problem.  

• June 29th 2026, 12:00 p.m. Room 012 Centro Didattico Morgagni, Luca Dieci (Professor at Georgia Tech)

Title: Optimal trajectories for optimal transport

Abstract: We present solution of a discrete optimal transport problem in a nonuniform environment. To solve the optimal transport problem, we build the cost matrix and then use classical solvers for discrete optimal transport. The main challenge is to form the cost matrix, which requires finding the optimal trajectory between two points, and for this task we formulate and solve the associated Euler-Lagrange equation. We provide verifiable sufficient conditions of optimality of the solution and validate numerically the computation of the cost matrix. We illustrate our results and performance of the algorithms on several numerical examples in 2 and 3 space dimensions, and also give extension of the results to the non-autonomous setting.

Joint work with Daniyar Omarov, University of Alberta-PIMS (Canada).