Bonmin

Bonmin is an open-source solver for mixed-integer nonlinear programming (MINLP), and is part of the COIN-OR project. It provides algorithms for solving problems that combine continuous and integer decision variables with nonlinear objective functions and constraints. Bonmin aims to find globally optimal solutions or to provide rigorous bounds in the presence of nonlinearities and discrete decisions.

The solver implements several solving frameworks, including Outer Approximation (OA), Nested Outer Approximation (NOA), and Branch-and-Bound methods that utilize nonlinear programming relaxations. In OA-based approaches, a sequence of NLP relaxations is solved to generate linearizations that approximate the nonlinear feasible region, with iterations that refine the approximation. NOA extends OA by introducing additional NLP subproblems to improve the representation of the feasible set. Branch-and-Bound mode performs a combinatorial search, solving NLP relaxations at each node to obtain bounds and prune suboptimal branches.

Bonmin relies on external nonlinear programming solvers to handle the NLP subproblems, with Ipopt commonly used, though it can interface with other COIN-OR-compatible NLP solvers as well. It integrates with modeling environments and solver ecosystems in COIN-OR, such as CoinUtils and Pyomo, to facilitate problem formulation and solver orchestration.

Typical applications span process optimization, energy systems, and engineering design, where decisions include discrete choices and nonlinear relationships. Bonmin is distributed under the COIN-OR open-source umbrella and is maintained to interoperate with other optimization tools in the project, providing a flexible option for solving MINLP problems.