Vocal Optimization Conference: Advanced Algorithms
June 5-7, 2024, Budapest, Hungary

Plenary Invited Speakers

Daniel Kuhn (College of Management of Technology, Swiss Federal Institute of Technology Lausanne)

Short bio: Daniel Kuhn is Professor of Operations Research at the College of Management of Technology at EPFL, where he holds the Chair of Risk Analytics and Optimization (RAO). Hi research interests are focused on data-driven optimization, as well as stochastic and robust optimization. Before joining EPFL, Daniel Kuhn was a faculty member in the Department of Computing at Imperial College London (2007-2013) and a postdoctoral research associate in the Department of Management Science and Engineering at Stanford University (2005-2006). He holds a PhD degree in Economics from University of St. Gallen and an MSc degree in Theoretical Physics from ETH Zurich. He is the editor-in-chief of Mathematical Programming.

Title: Distributionally Robust Linear Quadratic Control

Abstract: Linear-Quadratic-Gaussian (LQG) control is a fundamental control paradigm that is studied in various fields such as engineering, computer science, economics, and neuroscience. It involves controlling a system with linear dynamics and imperfect observations, subject to additive noise, with the goal of minimizing a quadratic cost function for the state and control variables. In this work, we consider a generalization of the discrete-time, finite-horizon LQG problem, where the noise distributions are unknown and belong to Wasserstein ambiguity sets centered at nominal (Gaussian) distributions. The objective is to minimize a worst-case cost across all distributions in the ambiguity set, including non-Gaussian distributions. Despite the added complexity, we prove that a control policy that is linear in the observations is optimal for this problem, as in the classic LQG problem. We propose a numerical solution method that efficiently characterizes this optimal control policy. Our method uses the Frank-Wolfe algorithm to identify the least-favorable distributions within the Wasserstein ambiguity sets and computes the controller's optimal policy using Kalman filter estimation under these distributions.

Máté Matolcsi (Department of Analysis and Operations Research, Budapest University of Technology and Economics, Rényi Institute)

Short bio: Máté Matolcsi is the head of the Department of Analysis at the HUN-REN Alfréd Rényi Institute of Mathematics, as well as professor at the Budapest University of Technology and Economics. His research interests are focused on various applications of Fourier analysis. For his recent results he was awarded the Frontiers of Science Award at the International Congress of Basic Sciences, 2023, and the Rényi Prize, 2023. He obtained his PhD degree in mathematics, at ELTE university, Budapest, 2003.

Title: Linear programming bounds for problems is discrete geometry

Abstract: Let us colour the points of the plane in such a way that the endpoints of any segment of length 1 have different colours. The least number of colours needed is called the chromatic number of the unit distance graph of the plane, and determining this number is the famous Hadwiger-Nelson problem. A linear relaxation of the problem arises if we allow "fractional colourings". In this talk we will review some recent results concerning the fractional chromatic number of the plane, and the density of subsets avoiding the unit distance. In all results the theoretical considerations yield linear programs, whose solution gives bounds on the relevant quantities. A computer search is then utilized to select the best possible parameters of the linear program to obtain the sharpest possible bounds.

François Glineur (Center for Operations Research and Econometrics, Catholic University of Louvain)

Short bio: François Glineur earned dual engineering degrees from CentraleSupélec and Université de Mons in 1997, and a PhD in Applied Sciences from the latter institution in 2001. After visiting Delft University of Technology and working as a post-doctoral researcher at McMaster University, he joined Université catholique de Louvain, where he is currently a full professor of applied mathematics in the Engineering School. He is also a member of the Center for Operations Research and Econometrics and the Institute of Information and Communication Technologies, Electronics and Applied Mathematics. He served as the Engineering School's vice-dean between 2016 and 2020. His primary areas of interest in research are optimization models and methods, with a particular emphasis on convex optimization and algorithmic efficiency. He received the 2017 Optimization Letters best paper award for the worst-case analysis of gradient descent with line search. He is also interested in the use of optimization in engineering, as well as nonnegative matrix factorization and its application to data analysis.

Title: Performance estimation of optimization methods: a guided tour

Abstract: Identifying the worst-case behaviour of an optimization method is a question that can itself be cast as an optimization problem. This is the main idea behind performance estimation, initially proposed by Yoel Drori and Marc Teboulle in 2014. In this framework, one seeks to compute the exact convergence rate of a given black-box optimization algorithm over a given class of problem instances. In many cases, including most fixed-step first-order algorithms, this computation can be reformulated into a finite-dimensional, tractable semidefinite program using necessary and sufficient interpolation conditions to describe functions involved in the problem. Solving this program provides an exact, unimprovable convergence rate, a mathematical proof guaranteeing this rate and a problem instance where this worst-case behaviour is achieved. While this computer-assisted procedure is based on numerical computations, many of the obtained results can later be converted into standard mathematical statements with analytical rates and independently checkable proofs. The knowledge of the exact worst-case behaviour of algorithms is useful to compare efficiency across methods, tune algorithmic parameters (such as step-size) and, ultimately, design new methods with improved behaviour, either using insights gained from the performance estimation procedure or with some automated method design techniques. In this talk we will survey a few of the main achievements in the area of performance estimation and showcase some recent results. The latter include the exact convergence rates of the gradient method over the full range of constant step-sizes, both on smooth (strongly) convex and smooth nonconvex functions, the performance of block-coordinate algorithms, how to deal with methods involving linear operators and the exact convergence rate of the last iterate in subgradient methods. We will also discuss some open questions related to performance estimation. This talk will present joint work with Nizar Bousselmi, Julien Hendrickx, Yassine Kamri, Ion Necoara, Panagiotis Patrinos, Teodor Rotaru and Moslem Zamani.

Merve Bodur (Operational Research, School of Mathematics, The University of Edinburgh)

Short bio: Merve Bodur is an Associate Professor in the School of Mathematics at the University of Edinburgh. She obtained her Ph.D. from the University of Wisconsin-Madison, her B.S. in Industrial Engineering and her B.A. in Mathematics from Bogazici University, Turkey. Her main research area is optimization under uncertainty, primarily for discrete optimization problems, with applications in a variety of areas such as scheduling, transportation, healthcare, telecommunications, and power systems. She serves on the editorial boards of Operations Research Letters, Omega, and INFOR. She is currently the Vice Chair/Chair-Elect of the INFORMS Computing Society, serves on the Committee on Stochastic Programming, and is a former Vice Chair of the INFORMS Optimization Society.

Title: Decision Rules for Sequential Decision-making Under Uncertainty

Abstract: Sequential decision-making emerges in a broad range of fields and is often impacted by uncertainty. Multistage stochastic programming (MSP) and multistage adjustable robust optimization (MSARO) are suitable modelling frameworks for sequential decision-making under uncertainty, among others. Those problems are theoretically and computationally challenging and, as such usually solved by means of approximations. In that regard, a commonly employed approach is decision rules (DRs), which restrict the policies to follow a certain functional form of the observed random outcomes. In this talk, we will review traditional as well as recently proposed primal and dual DRs for general MSP and MSARO problems. Our review will include two-stage DRs and Lagrangian dual DRs, which make solution algorithms designed for two-stage problems amenable to generating high-quality policies for multistage problems. In particular, for MSPs with potentially mixed-integer recourse, our review will also feature a Markov-chain-based variant of two-stage DRs to leverage the underlying stochastic process and a certain class of mixed-integer DRs for nonlinear MSPs with a large number of stages. The latter, by design, leads to smooth restricted problems (making stochastic gradient decent methods amenable) and highly interpretable decision policies. We will present numerical results on applications from various domains to illustrate the presented ideas.