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Efficient methods for structured nonconvex optimization and optimization under inexact oracles by Guillaume VAN DESSEL -
Vendredi 27 juin 2025 à 16h00 - Auditoire BARB91 - Place Sainte-Barbe - 1348 Louvain-la-Neuve
This thesis revolves around three main optimization frameworks, each accounting for one thesis part. In each of them, contributions are spread among theoretical results and fully implementable algorithms. Notably, a particular emphasis has been put throughout this work to either propose parameter-free methods or to specify how to fix the values of an algorithms' parameters.
The first part about Tunable Oracle Methods addresses the problem of optimally coping with inexact updates/information within traditional methods when inexactness is controllable and its (worst-case) impact predictable. Based on an assumed relationship linking the computational cost invested at a given iteration and the level of inexactness incurred, we derive optimal inexactness schedules for a given total computational budget.
In the second part about Difference-of-Convex Methods, we highlight various substructures of generic Difference-of-Convex (DC) objectives (e.g. Sum of Minimum-of-Convex) to which individual chapters are dedicated. (DC) objectives represent a broad class of nonconvex and generally nonsmooth functions that enhance and extend the modelling power of convex ones. Their optimization is thereby practically very attractive but unfortunately computationally really difficult. Within each of the aforementioned chapters, we endow the substructure with a specific minimization oracle. Computing these oracles always amount to solving some convex optimization problem. Then, we analyze what can be achieved with the oracle at hand and how it can be best exploited to harvest the best objective values in reasonable computational times.
In the last part about Chance-Constrained Programs (CCP), we present presolve techniques for optimization problems that exhibit a single probabilistic constraint. We focus on the finite-support case, i.e. the random parameter involved in the formulation can take any value among several possible scenarios. Such (CCP) are usually reformulated as mixed-integer convex programs involving binary variables. Under the assumption of quasi-convexity of the probabilistic constraint with respect to the random parameter, we use some geometric arguments in the parameter-space leading to sufficient conditions to reduce the number of binary variables used. These conditions dramatically speed-up the solving of the aforementioned mixed-integer convex programs.
Jury members :
Prof. François Glineur (UCLouvain) (Supervisor)
Prof. Jean-Charles Delvenne (UCLouvain) (Chairperson)
Prof. Pierre-Antoine Absil (UCLouvain) (Secretary)
Prof. Yurii Nesterov (UCLouvain)
Prof. Hoai-An Le Thi (Université de Lorraine)
Dr. Welington de Oliveira (Mines Paris PSL)
Pay attention : the public defense of Guillaume VAN DESSEL will also take place in the form of a videoconference