The 27th Conference on Integer Programming and Combinatorial Optimization — June 17–19, 2026, Padova, Italy
Summer School
The IPCO 2026 Summer School takes place June 15–16 in room 1A150 of the Department of Mathematics "Tullio Levi-Civita" (63 Via Trieste, Padova), a short walk from the conference venue (see the Local Information page for details).
Monday, June 15, 2026
8:15–8:45 Registration
8:45–9:00 Summer school opening
9:00–10:30 Oktay Günlük — Two graph problems related to quantum compiling: qubit routing and parallel token swapping
10:30–11:00 Coffee break
11:00–12:30 Margarida Carvalho — Duality-based reformulations in bilevel optimization, Part I
12:30–14:15 Lunch break
14:15–15:45 Alberto Del Pia — Mixed integer quadratic programming I: Structural properties
15:45–16:15 Coffee break
16:15–17:30 Free discussion
Tuesday, June 16, 2026
9:00–10:30 Margarida Carvalho — Duality-based reformulations in bilevel optimization, Part II
10:30–11:00 Coffee break
11:00–12:30 Alberto Del Pia — Mixed integer quadratic programming II: Algorithms and complexity
12:30–14:15 Lunch break
14:15–15:45 Oktay Günlük — Mixing set and its extensions
15:45–16:15 Coffee break
16:15–17:30 Free discussion
Speakers and Abstracts
Margarida Carvalho, Université de Montréal — Duality-based reformulations in bilevel optimization (Parts I and II)
Bilevel optimization models hierarchical decision-making between a leader and one or more followers. These two lectures build up duality-based reformulation techniques, moving from classical linear settings to more complex mixed-integer ones. Part I introduces core terminology and solution concepts, discusses the computational complexity of bilevel problems, and covers single-level reformulations for the linear-follower case via KKT conditions and strong duality, before examining the polyhedral structure of the bilevel feasible set and its use in integer programming games. Part II extends these ideas to settings where the lower-level problem is nonlinear or nonconvex, including monotropic-programming followers arising in equilibrium problems, and surveys recent dynamic-programming based reformulations for mixed-integer bilevel programs, an area that remains largely open for further research.
Alberto Del Pia, University of Wisconsin-Madison — Mixed integer quadratic programming (Parts I and II)
Mixed Integer Quadratic Programming (MIQP) minimizes a quadratic function over a polyhedron with a subset of variables restricted to integers, extending both mixed-integer linear programming and quadratic programming, and it appears in a wide variety of applications. These lectures survey recent theoretical progress on MIQP. Part I covers structural properties such as the attainability of optimal solutions, rationality and encoding size, the role of unbounded directions, and links to complexity classes including NP. Part II turns to algorithmic results, highlighting exact and approximation methods that come with provable performance guarantees.
Oktay Günlük, Georgia Institute of Technology — Two graph problems related to quantum compiling; Mixing set and its extensions
The first lecture looks at the qubit assignment and routing problem that arises when mapping a logical quantum circuit onto hardware with limited two-qubit connectivity, framing it as a combinatorial reconfiguration problem on a graph. Integer programming models are presented along with numerical results on several hardware topologies that outperform SABRE, the standard heuristic used in Qiskit. The talk then turns to a related, simpler reconfiguration problem called parallel token swapping, which seeks an optimal sequence of vertex-disjoint swaps between token configurations on a graph, along with an analysis of a natural lower bound useful for heuristic design. The second lecture reviews mixing sets, first introduced for lot-sizing problems and later generalized to the integer setting, along with their many extensions. It covers the polyhedral description of these sets, their connection to mixed-integer rounding and split cuts, efficient separation procedures, and recent developments including polymatroid-related extensions and an application to a boxing problem.