Hi Shanshan,
MindtPy currently implements methods for guaranteeing optimality in both convex and nonconvex MINLP problems, depending on the algorithm that you are using. We can modify the algorithm by the option “strategy” where “OA” is the default. The strategies “OA” and “ECP”, which stand for Outer approximation and extended cutting planes respectively, have convergence guarantees for convex MINLP problems. The strategy “GOA”, which stand for global outer approximation” implements methods that guarantee convergence for nonconvex MINLP problems. Be aware that GOA requires you to download and install MC++ in your system https://pyomo.readthedocs.io/en/stable/contributed_packages/mcpp.html , and that the NLP subproblems need to be solved to global optimality (using solvers such as BARON or SCIP) to actually provide you with a global optimal solution. Usually the methods for convex MINLP are used as heuristics for nonconvex MINLP, with decent performance in practice (let me shamelessly plug a link to this review paper on convex MINLP https://link.springer.com/article/10.1007/s11081-018-9411-8 )
I hope this helps!
Best regards,
David E. Bernal
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