Invited Speakers

• BUCHHEIM Christoph (Technische Universität Dortmund, Germany)

• GHADDAR Bissan (IE University and Ivey Business School, Spain)

• GRÜNE Lars (Universität Bayreuth, Germany)

• IUTZELER Franck (Université de Toulouse, France)

Christoph Buchheim

Technische Universität Dortmund, Germany

Combinatorial Optimization in Function Space

Optimal control problems with discrete-valued controls are typically tackled via a first-discretize-then-optimize strategy, in which the original infinite-dimensional problem is approximated by a large-scale finite-dimensional mixed-integer nonlinear program (MINLP) and handed to a general-purpose solver. A fundamental drawback of this approach is that conventional discretization schemes shrink the feasible set, so that dual bounds on the discretized problem are not valid in general for the original infinite-dimensional formulation. Moreover, such bounds do not carry over when the mesh is refined. Although one can in principle correct for this by estimating the discretization error, the resulting procedure is both technically involved and tends to produce only weak bounds.

To overcome these limitations and to support a branch-and-bound-and-refine scheme for global optimization in function space, we introduce a first-dualize-then-discretize paradigm. In this framework, a convex relaxation of the original problem is dualized directly in function space; the resulting dual problem can then be discretized with any conforming scheme, and the dual objective value of the discretized dual problem constitutes a valid lower bound for the original infinite-dimensional problem. We demonstrate the approach on two classes of problems featuring total variation or minimum dwell-time constraints, for which we also provide extended formulations in function space.

Bissan Ghaddar

IE University, Ivey Business School, Spain

Sparse Relaxations and Learned Structure for Large-Scale Polynomial Optimization

Polynomial optimization problems (POPs) arise in numerous domains such as energy systems and water networks, yet their nonconvexity poses major computational challenges. This talk focuses on exploiting sparsity structures to enable scalable global optimization of large-scale POPs. We develop formulations that leverage correlative sparsity to construct structured semidefinite and second-order cone relaxations of significantly reduced dimensionality.

We further explore machine learning models that learn variable dependencies in order to guide sparsity-pattern selection. By exploiting chordal extensions of the sparsity graph and decomposing the semidefinite matrices, the resulting sparse relaxations achieve tight bounds at tractable computational cost. Computational results on optimal power flow instances demonstrate the effectiveness of the approach.

Lars Grüne

University of Bayreuth, Germany

Performance of Deterministic and Stochastic Model Predictive Control

Model Predictive Control (MPC) is one of the most successful modern control techniques. It generates a feedback control by successively solving finite-horizon optimal control problems. A key question is whether the resulting feedback is approximately optimal in some sense. In this talk we give a positive answer to this question using dissipativity and turnpike properties.

We first describe results for deterministic MPC, then present an industrial use case, and finally give a survey on recent results for stochastic MPC schemes.

Frantz Iutzeler

Université de Toulouse, France

Around distributional robustness and generalization in stochastic optimization

Transferring predictive power from past data to similar future situations is a central objective in statistical learning and stochastic optimization.  In the past years, distributionally robust optimization has become popular by providing a mathematically elegant proxy for this problem by relying on optimal transport between distributions. We will cover recent advances on this approach but also its limitation in deep learning and related perspectives.