Abstracts

Francesca Maggioni:
Bounds and Approximations for Large Scale Optimization Problems Under Uncertainty

Many real world decision problems are dynamic and affected by uncertainty. Stochastic Programming provides a powerful approach to handle this uncertainty within a multi-period decision framework. However, as the number of stages increases, the computational complexity of these problems grows exponentially, posing significant challenges. To tackle this, approximation techniques are often used to simplify the original problem, providing useful upper and lower bounds for the objective function’s optimal value.
This talk explores methods for generating bounds for a wide variety of problem structures affected by uncertainty. We begin by discussing bounds based on scenario grouping under the assumption that a sufficiently large scenario tree is given but is unsolvable, both in the context of stochastic programming and distributionally robust optimization. Next, we extend these techniques to address more complex problems, including multi-horizon stochastic optimization and decision-dependent stochastic optimization.
Finally, the talk introduces the integration of these bounding methods with Benders’ decomposition. To reduce the computational burden of generating a cut for each scenario, a Benders refinement-chain cuts method is proposed, where scenario subsets are used to generate group-wise optimality cuts. This aggregation significantly lowers the number of cuts required, while preserving valid lower bounds. Theoretical relationships between cuts generated at different refinement levels are established.
Numerical experiments on various energy and transportation optimization problems demonstrate the efficiency of the proposed approaches.

Tobias Sutter:
Recursive Frank-Wolfe Optimization with Learned Domains and Objectives

We study a data-driven variant of the classical Frank-Wolfe algorithm for convex optimization over compact convex domains. In contrast to the standard setting, both the feasible domain and the objective function are initially unknown and must be learned from data during the optimization process. Our method incorporates statistical estimators directly into the Frank-Wolfe iterations, thereby preserving the projection-free nature of the classical algorithm while adapting to uncertainty in the problem formulation. We prove convergence guarantees showing that the optimization error is controlled by the accuracy of the learned domain and objective estimators. Numerical experiments illustrate that the proposed recursive Frank-Wolfe method can achieve convergence behavior comparable to the classical algorithm with exact problem knowledge, while offering significant computational savings in data-driven settings.

This is joint work with Marcel Kaiser, University of Konstanz.