Plenary Speakers

Title: Deterministic global optimisation of mixed integer nonlinear bilevel programs

Abstract: Bilevel optimization problems are relevant to numerous applications, including economics, planning and a range of engineering problems (parameter estimation, flexibility analysis). We present a deterministic global optimisation algorithm, the Branch-and-Sandwich algorithm, for bilevel problems with nonlinear outer and inner problems. This branch-and-bound approach is based on the formulation of bounding problems for the inner and outer problems, together with a branching/tree management strategy that allows branching on the inner variables. We present an extension of the algorithm to mixed-integer problems and introduce BASBL, our implementation within the open-source MINOTAUR framework. We also introduce BASBLib, an extensive online library of bilevel benchmark problems collected from the literature including problems derived from practical applications and designed to enable contributions from the bilevel optimization community. We use the problems from BASBLib to analyze the performance of BASBL using different algorithmic options, including different bounding schemes, branching, and node selection strategies.

(credits to Remigijus Paulavičius and Polyxeni-Margarita Kleniati)

Title: Interior Point Methods and Beyond

Abstract: In this talk I will discuss an impact made by interior point methods (IPMs) for optimization. IPMs deliver efficient and reliable solution techniques for linear, quadratic, nonlinear, second-order cone and semidefinite programming problems and excel when dimensions of problems are large. They also provide an inspiration for a design of more general schemes for solving other classes of optimization problems by using an inexact Newton method embedded into a continuation scheme.

Title: Wasserstein Distributionally Robust Optimization: Theory and Applications in Machine Learning

Absract: Many decision problems in science, engineering and economics are affected by uncertain parameters whose distribution is only indirectly observable through samples. The goal of data-driven decision-making is to learn a decision from finitely many training samples that will perform well on unseen test samples. This learning task is difficult even if all training and test samples are drawn from the same distribution – especially if the dimension of the uncertainty is large relative to the training sample size. Wasserstein distributionally robust optimization seeks data-driven decisions that perform well under the most adverse distribution within a certain Wasserstein distance from a nominal distribution constructed from the training samples. In this talk we will argue that this approach has many conceptual and computational benefits. Most prominently, the optimal decisions can often be computed by solving tractable convex optimization problems, and they enjoy rigorous out-of-sample and asymptotic consistency guarantees. We will also show that Wasserstein distributionally robust optimization has interesting ramifications for statistical learning and motivates new approaches for fundamental learning tasks such as classification, regression, maximum likelihood estimation or minimum mean square error estimation, among others.

Title: Teaching Numerical Optimization: How to Move from Theory to Code?

Abstract: Those who teach numerical optimization almost always start with theory. But it is also important for students to learn about computational and software issues that arise in writing code for solving real-world problems. This talk will discuss a variety of ideas for achieving this often-overlooked transition.