vecmin f(x) subject to h(x)=0, g(x)>=0,

n=dim(x), m=dim(g), p=dim(h).

Many problems in real life are multiple criteria decision problems. These are usually solved by proper scalarization and parametrization. The vecmin means usually a Pareto optimum. An optimum in the sense of the natural halforder of R^n need not exist.

**Solvers which explicitly provide for multiple objectives are**

MOSQP |
SQP method for differentiable constrained NLPs, AMPL interface (Matlab) |

PolySciP |
solver for multi-criteria integer programming and multi-criteria linear programming with an arbitrary number of objectives |

NSGA-II |
evolutionary method (Matlab) |

LIONsolver |
reactive search, free for research |

PaGMO/PyGMO |
Parallel Global Multiobjective Optimizer (C++/Python) |

MCDM |
Overview of commercial and other MCDM software |

MOEA |
Multiobjective optimization framework in Java |

NDA_PMIN |
An SQP variable metric method for minimax optimization, linear constraints. |

NLPJOB |
Interactively changeable scalarization and solution by NLPQL |

CONMAX (f77) |
uses ODEs to generate search direction followed by Newton to correct back to feasible region, authors claim it is very robust but somewhat slow. |

NIMBUS |
to be used interactively through a web-interface ,allows nonsmooth problems, uses bundle method |

NBI |
Normal Boundary Intersection (Matlab) |

jMetal |
extensive Multiple-Objective MetaHeuristics library in Java |

EMOO |
Evolutionary Multi-objective Optimization (Python, MPI) |

SPEA |
Strength Pareto Evolutionary Algorithm (C++) |

SPEA-TSP |
SPEA implementation for the TSP (C++) |

HIPRE 3+ |
Decision analytic tool for Windows 95/98/NT |

MCMA |
From IIASA. Linear multiobjective problems. Needs HOPDM and others. only binaries for Solaris 2.5 and Windows 95. |

FGM/RGM |
Linear and nonlinear problems; feasible/resonable goals method. Windows binaries. |