Elisabeth Gaar, Jon Lee, Ivana Ljubic, Markus Sinnl, Kübra Taninmis Ersüs,
"SOCP-Based Disjunctive Cuts for a Class of Integer Nonlinear Bilevel Programs"
, in Aardal, Karenand Sanit\`a, Laura: Integer Programming and Combinatorial Optimization, Serie Lecture Notes in Computer Science (LNCS), Springer International Publishing, Cham, Seite(n) 262-276, 2022, ISBN: 978-3-031-06901-7
Original Titel:
SOCP-Based Disjunctive Cuts for a Class of Integer Nonlinear Bilevel Programs
Sprache des Titels:
Englisch
Original Buchtitel:
Integer Programming and Combinatorial Optimization
Original Kurzfassung:
We study a class of bilevel integer programs with second-order cone constraints at the upper level and a convex quadratic objective and linear constraints at the lower level. We develop disjunctive cuts to separate bilevel infeasible points using a second-order-cone-based cut-generating procedure. To the best of our knowledge, this is the first time disjunctive cuts are studied in the context of discrete bilevel optimization. Using these disjunctive cuts, we establish a branch-and-cut algorithm for the problem class we study, and a cutting plane method for the problem variant with only binary variables. We present a preliminary computational study on instances with no second-order cone constraints at the upper level and a single linear constraint at the lower level. Our study demonstrates that both our approaches outperform a state-of-the-art generic solver for mixed-integer bilevel linear programs that is able to solve a linearized version of our test instances, where the non-linearities are linearized in a McCormick fashion.