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Software

Here is a list of software packages that can cope with optimisation problems that have both discrete and nonlinear aspects:

  • ALPHA-ECP is an exact solver for Mixed-Integer Non-Linear Programs with 'pseudo-convex' objective and constraint functions.  The underlying algorithm is the 'extended cutting plane' method.
  • BARON is a software package for general Mixed-Integer Non-Linear Programs.  Several exact algorithms are available, all based on the 'branch-and-reduce' paradigm.  See also the BARON manual.
  • BONMIN is a software package for general Mixed-Integer Non-Linear Programs.  Several algorithms are available.  They are exact when the problem is convex, and heuristic otherwise.
  • COUENNE is an exact solver for general Mixed-Integer Non-Linear Programs.  The underlying algorithm is branch-and-reduce.
  • CPLEX now has an exact solver for convex Mixed-Integer Quadratically-Constrained Programs.  The method used appears to be branch-and-bound with convex quadratic relaxations.
  • DICOPT is a solver for general Mixed-Integer Non-Linear Programs.  The underlying algorithm is 'outer approximation'.  It is exact when the problem is convex, and heuristic otherwise. 
  • FilMINT is an exact solver for convex Mixed-Integer Non-Linear Programs. The underlying algorithm is 'LP/NLP based branch-and-bound'.
  • LaGO is a solver for general Mixed-Integer Non-Linear Programs, based on Lagrangian Decomposition and Branch-and-Bound.  The algorithm is exact when the problem is convex, and heuristic otherwise.
  • LINDO API now has an exact solver for convex Mixed-Integer Quadratic Programs.  The method used appears to be branch-and-bound with quadratic programming relaxations.
  • MINLPBB is an exact solver for convex Mixed-Integer Non-Linear Programs.  The underlying algorithm appears to be branch-and-bound with convex programming relaxations.
  • MINOPT is a software package for convex Mixed-Integer Non-Linear Programs.  Several exact algorithms are available. 
  • MOSEK now has an exact solver for Mixed-Integer Second-Order Conic Programs.  The method used appears to be branch-and-bound with conic relaxations.
  • SCIP can now solve Mixed-Integer Quadratically-Constrained Programs.  It is not yet clear whether the problem must be convex, or what kind of solution method is used.

Note: BONMIN, COUENNE, LaGO and SCIP are free.