In this talk, we provide an overview of Gurobi's algorithmic
components for solving nonlinear optimization problems to global
optimality. In essence, we extend our existing mixed-integer
programming (MIP) framework to handle such problems. This includes our
presolve algorithms, an extension of the branch-and-bound method
utilizing spatial relaxations, and an interior point algorithm for
nonlinear problems, which serves as a primal heuristic to find
high-quality solutions. As a result, we can compute solutions to
nonlinear optimization problems along with certificates for global
optimality.
Finally, we have extended gurobipy to facilitate the easy formulation
of expression-based nonlinear optimization problems in Python.
Gurobi's nonlinear solver applies to explicit expression-based
constraints and does not require the supply of derivative data.
