Every optimization problem has a corresponding verification problem that checks whether a given optimal solution is in fact optimal. In the literature, there are a lot of such ways to verify optimality for a given solution, for example, the branch-and-bound tree. To simplify this task, optimality certificates were introduced for convex mixed-integer nonlinear programs, and it was shown that the sizes of the certificates are bounded in terms of the number of integer variables. We introduce an algorithm to compute the certificates and conduct computational experiments. Through the experiments, we show that the optimality certificates can be surprisingly small. History: Accepted by Andrea Lodi, Area Editor for Design & Analysis of Algorithms—Discrete. Funding: This work was supported by the Deutsche Forschungsgemeinschaft [CRC 154 Subproject A05, CRC 154 Subproject B07, and SFB Transregio 154], the Bundesministerium für Wirtschaft und Energie. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2022.0099 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2022.0099 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

The SCIP Optimization Suite provides a collection of software packages for mathematical optimization centered around the constraint integer programming framework SCIP . The focus of this article is on the role of the SCIP Optimization Suite in supporting research. SCIP ’s main design principles are discussed, followed by a presentation of the latest performance improvements and developments in version 8.0, which serve both as examples of SCIP ’s application as a research tool and as a platform for further developments. Furthermore, this article gives an overview of interfaces to other programming and modeling languages, new features that expand the possibilities for user interaction with the framework, and the latest developments in several extensions built upon SCIP .