Best SICON Paper Prize 2021

Doctoral student Lukas Hertlein and Professor Michael Ulbrich from the Department of Mathematics at the Technical University of Munich (TUM) are the winners of the "SIAM Activity Group on Control and Systems Theory Best SICON Paper Prize 2021" of the Society for Industrial and Applied Mathematics (SIAM). The prize will be awarded at the "SIAM Conference on Control and Its Applications (CT21)". The conference will be held virtually from 19 to 21 July 2021.

Hertlein and Ulbrich will receive the prize for their paper titled "An Inexact Bundle Algorithm for Nonconvex Nonsmooth Minimization in Hilbert Space''. In this scientific work, they develop a bundle method for nonsmooth nonconvex optimization problems in infinite-dimensional Hilbert spaces. They will present the work in a talk at CT21 on 20 July 2021 at 18:00 (12:00 pm EDT).

An Inexact Bundle Algorithm for Nonconvex Nonsmooth Minimization in Hilbert Space

Models for complex systems often exhibit non-smooth behavior, such as involving systems of inequalities. In many applications, for example contact mechanics, these systems are infinite-dimensional. Motivated by the goal of optimally controlling or designing such systems, Hertlein and Ulbrich develop a bundle method in their work. This can solve a comprehensive class of nonsmooth, nonconvex, and infinite-dimensional optimization problems.

The approach allows for inexactness in the computation of function values and subgradients and thus makes it possible to implement adaptive error control. Hertlein and Ulbrich develop for the first time a global theory of convergence in a nonconvex infinite-dimensional framework. They illustrate their results by applications to optimal control of obstacle problems.

The award-winning paper, "An Inexact Bundle Algorithm for Nonconvex Nonsmooth Minimization in Hilbert Space," appeared in the 2019 SIAM Journal on Control and Optimization (SICON). The paper is at the interface of numerical optimization methods, nonsmooth analysis, and functional analysis. It was funded by the DFG as part of the priority program SPP 1962, where Ulbrich is Principal Investigator in the (now completed) project "Optimization Methods for Mathematical Programs with Equilibrium Constraints in Function Spaces based on Adaptive Error Control and Reduced Order or Low Rank Tensor Approximations" and in the ongoing project "Theory and Solution Methods for Generalized Nash Equilibrium Problems Governed by Networks of Nonlinear Hyperbolic Conservation Laws."

The Winners

Lukas Hertlein is doing his doctorate at TUM under Michael Ulbrich. His research focuses on the development of algorithms that allow the use of inexact function values and subgradients, and applications to optimal control of obstacle problems.

Michael Ulbrich is a professor of mathematical optimization in our department. His research interests include mathematical optimization, optimal control, numerical optimization methods, nonsmooth analysis, and applications to engineering and other fields. He is a member of the TUM Senate and the TUM Board of Trustees.

About the Best SICON Paper Prize

The SIAM Activity Group on Control and Systems (SIAG/CST) has awarded the Best SICON Paper Prize in the form of a plaque every two years since 2007 to the authors of the two most outstanding papers published in SICON in the three calendar years preceding the year of the award. The papers must make a significant research contribution to the field of control and systems theory.

Each award committee consists of five members of SIAG/CST nominated by the Chair. The selection committee for the 2021 prize consists of: Francois Dufour (Chair), University of Bordeaux; Pauline Barrieu, London School of Economics; Fariba Fahroo, AFOSR; Rafal Goebel, Loyola University Chicago; and Chao Zhu, University of Wisconsin-Madison.

For details on the 2021 awardees, see the SIAM Newsblog.