The workshop took place from July 1 to 3, 2026, in room V.1.01 of Alpen-Adria-Universität Klagenfurt.
It was dedicated to using conic approaches for solving nonconvex quadratic optimization problems with uncertainty. Researchers from the FWF-funded project Uncertain QCQP, as well as other researchers working on conic optimization, gathered for discussions and presentations of open problems and new results. The presentations triggered lively discussions that opened new research directions. In particular the early career researchers received a lot of valuable feedback.
Programme:
Johannes Schmucker opened the workshop and presented his joint work with Daniel Brosch where they exploit symmetry and term-sparsity of polynomial optimization problems. This was followed by Immanuel Bomze’s talk on conic duality and attainability of simplicial quadratic optimization problems, where he did not use any arguments from convex analysis but purly algebraic ones. These results come from joint work with E. Alper Yıldırım. The last presentation of the day was given by Angelika Wiegele. She presented an integer SDP formulation of the Quadratic Minimum Spanning Tree Problem and an algorithm following the Peaceman Rachford Splitting scheme for solving the resulting relaxations. This work stems from cooperation with Frank de Meijer, Melanie Siebenhofer and Renata Sotirov.
The day was closed with a dinner at the beautiful lake Wörthersee.
The second day started with Johannes Zischg who introduced in this talk a 2.5 stage adjustable robust optimization problem and formulated it as a copositive programming problem. This was jointly done with Immanuel Bomze and Markus Gabl. Daniel Brosch presented work he did together with Sven Polak, where they computed the upper bound 155 for the Ramsey number R(6,6), using polynomial optimization and heavy machinery for symmetry reduction. Franz Rendl investigated relaxtions between the Lasserre hierarchy and the exact subgraph hierarchy for max-cut problems. The scientific part of the workshop was closed by Markus Gabl’s talk on the algorithm of Stefan Bundfuss and Mirjam Dür for solving copositive programming problems. After these intensive two days of presentations and discussions, the participants enjoyed a swim in Lake Wörthersee.
On the third day, the workshop was summarized during a hike to the mountain Kosiak and to Klagenfurter Hütte.
List of Participants: Immanuel Bomze, Daniel Brosch, Markus Gabl, Franz Rendl, Johannes Schmucker, Angelika Wiegele, Johannes Zischg.
For more information on this workshop, contact angelika [dot] wiegele [at] aau [dot] at.
