Dipartimento di Ingegneria informatica, automatica e gestionale

Prof. Wiegele will teach the following 10 hours PhD course

Bio:  Angelika Wiegele is a mathematician working on semidefinite optimization and combinatorial optimization. She is Professor at the Mathematics Department at Alpen-Adria-Universität Klagenfurt. Angelika studied mathematics in Klagenfurt, London, and Eindhoven. She earned her master in mathematics (2001) and her Ph.D. in mathematics (2006) at Alpen-Adria-Universität Klagenfurt. She held research and/or teaching positions in Graz (Department of Mathematics), Klagenfurt (Department of Mathematics), Rome (IASI-CNR) and Cologne (Institut f. Informatik). She was visiting professor at the Università degli Studi di Roma "Tor Vergata", Department of Civil  Engineering and Computer Science Engineering in fall 2019. In the years 2022 until 2024 she was member of the Global Faculty of the University of Cologne. Her research bridges theory and practical computation, and she has published extensively in optimization journals. She has also successfully acquired third-party funded projects, most notably as the coordinator of the MSCA doctoral network ALMOA, a Marie Skłodowska-Curie Actions network that trains doctoral researchers in optimization.

Abstract: Semidefinite programming (SDP) extends linear programming to optimization over the cone of positive semidefinite matrices, and it has become a central tool for obtaining strong relaxations of hard combinatorial problems. This course offers a compact introduction to the theory, the algorithms, and the applications of SDP. We begin with the necessary background in linear algebra, convex sets, and positive semidefinite matrices, and then develop the foundations of semidefinite programming, including duality theory. The algorithmic part of the course covers two complementary approaches: interior point methods, which deliver high-accuracy solutions for small to medium-sized problems, and alternating direction methods, which scale to much larger instances at lower accuracy. The course concludes by showing how classical combinatorial optimization problems can be modeled as integer semidefinite programs and how their semidefinite relaxations yield strong bounds. The course is aimed at students and researchers in mathematics, computer science, and operations research who have a basic background in linear algebra and optimization.