@article{MuellerMunozGasseetal., author = {M{\"u}ller, Benjamin and Mu{\~n}oz, Gonzalo and Gasse, Maxime and Gleixner, Ambros and Lodi, Andrea and Serrano, Felipe}, title = {On generalized surrogate duality in mixed-integer nonlinear programming}, series = {Mathematical Programming}, volume = {192}, journal = {Mathematical Programming}, number = {1-2}, publisher = {Springer Berlin Heidelberg}, issn = {0025-5610}, doi = {10.1007/s10107-021-01691-6}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:523-16741}, pages = {89 -- 118}, abstract = {The most important ingredient for solving mixed-integer nonlinear programs (MINLPs) to global ϵ-optimality with spatial branch and bound is a tight, computationally tractable relaxation. Due to both theoretical and practical considerations, relaxations of MINLPs are usually required to be convex. Nonetheless, current optimization solvers can often successfully handle a moderate presence of nonconvexities, which opens the door for the use of potentially tighter nonconvex relaxations. In this work, we exploit this fact and make use of a nonconvex relaxation obtained via aggregation of constraints: a surrogate relaxation. These relaxations were actively studied for linear integer programs in the 70s and 80s, but they have been scarcely considered since. We revisit these relaxations in an MINLP setting and show the computational benefits and challenges they can have. Additionally, we study a generalization of such relaxation that allows for multiple aggregations simultaneously and present the first algorithm that is capable of computing the best set of aggregations. We propose a multitude of computational enhancements for improving its practical performance and evaluate the algorithm's ability to generate strong dual bounds through extensive computational experiments.}, subject = {Kombinatorische Optimierung}, language = {en} } @article{BolusaniBesanconGleixneretal., author = {Bolusani, Suresh and Besan{\c{c}}on, Mathieu and Gleixner, Ambros and Berthold, Timo and D'Ambrosio, Claudia and Mu{\~n}oz, Gonzalo and Paat, Joseph and Thomopulos, Dimitri}, title = {The MIP Workshop 2023 Computational Competition on reoptimization}, series = {Mathematical Programming Computation}, volume = {16}, journal = {Mathematical Programming Computation}, number = {2}, publisher = {Springer Nature}, address = {Berlin/Heidelberg}, issn = {1867-2949}, doi = {10.1007/s12532-024-00256-w}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:523-19804}, pages = {255 -- 266}, abstract = {This paper describes the computational challenge developed for a computational competition held in 2023 for the 20thanniversary of the Mixed Integer Programming Workshop. The topic of this competition was reoptimization, also known as warm starting, of mixed integer linear optimization problems after slight changes to the input data for a common formulation. The challenge was to accelerate the proof of optimality of the modified instances by leveraging the information from the solving processes of previously solved instances, all while creating high-quality primal solutions. Specifically, we discuss the competition's format, the creation of public and hidden datasets, and the evaluation criteria. Our goal is to establish a methodology for the generation of benchmark instances and an evaluation framework, along with benchmark datasets, to foster future research on reoptimization of mixed integer linear optimization problems.}, language = {en} }