# BMIBNB

Built-in solver for nonconvex problems

### In YALMIP

BMIBNB is invoked by using 'bmibnb' as solver flag in sdpsettings

### Comments

BMIBNB is an implementation of a standard branch & bound algorithm for nonconvex problems, based on linear programming relaxations and convex envelope approximations

The solver relies on external linear, quadratic and semidefinite programming solvers for solving the lower bounding relaxation problems, and nonlinear solvers for the upper bound computations.

Do not expect too much. Global solutions are extremely hard to compute, and this is a fairly simple implementation. Problems with more than 10 variables is often beyond the capabilities of this solver, although you might be lucky.

Most important options

`sdpsettings('bmibnb.roottight',[0|1])` |
Improve variable bounds at root-node by performing bound strengthening based on the full relaxed model (Can be very expensive, but lead to improved branching) |

`sdpsettings('bmibnb.lpreduce',[0|1])` |
Improve variable bounds in all nodes by performing bound strengthening using only the scalar constraints (including scalar cut constraints) in the model (Can be very expensive, but lead to improved branching, in particular for semidefinite problems) |

`sdpsettings('bmibnb.lowersolver', solvertag)` |
Solver for relaxed problems. |

`sdpsettings('bmibnb.uppersolver', solvertag)` |
Local solver for computing upper bounds. |

`sdpsettings('bmibnb.lpsolver', solvertag)` |
LP solver for bound strengthening
(only used if `bmibnb.lpreduce` is set to 1) |

`sdpsettings('bmibnb.numglobal', [int](/command/int))` |
A major computational burden along the branching process is to
solver the upper bound problems using a local nonlinear solver. By
setting this value to a finite value, the local solver will no
longer be used when the upper bound has been improved `numglobal` times.
This option is useful if you believe your local solver quickly gives
globally optimal solutions. It can also be useful if you have a
feasible solution and just want to compute a gap. In this case, use
the `usex0` option and set `numglobal` to 0. |

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