# interalg bench

### From OpenOpt

## Contents |

BARON (version 9.0.7. Built: LNX Mon Oct 4 13:04:39 EDT 2010, with GAMS Rev 236 LEX-LEI 23.6.0 x86_64/Linux) results were obtained on NEOS server

interalg (version **0.17** from 2011-March-27), Direct (version 4.0 from 2004-06-21) and intsolver (2009-02-13) results were obtained on AMD Athlon 3800+.

Test for intsolver and Direct were made with MATLAB 7.11.0 (R2010b); also, intsolver requires intlab (latest V. 6.0 was involved; license: free for noncommercial).

All solvers parameters hasn't been modified (default values were used).

# Box-bounded problems

## Test 1

a / (b + 10^{-15}) + c / (d + 10^{-15}) + e / (f + 10^{-15}) + f / (a + 10^{-15}) -> min

Required accuracy: 10^{-9}

All variables are bounded by 0 <= var <= 1

Optimal value: 0 (achived in points with a, c, e, f = 0 and any values of b, d)

BARON | Direct | intsolver | interalg | |
---|---|---|---|---|

Elapsed Time, sec | 1000 | 403 | 0.2 | 29 |

Objective value | 0.11 | 0.66 | F | 4.5 * 10^{-10} |

Source & log | >>> | >>> | >>> | >>> |

BTW, interalg works even with replacing 10^{-15} by 10^{-300} while BARON fails with 10^{-16}

## Test 2

a / (b + 10^{-15}) + c / (d + 10^{-15}) + e / (f + 10^{-15}) + f / (a + 10^{-15}) + 10^{-7} * (a + b + c + d + e + f)-> min

Required accuracy: 10^{-9}

All variables are bounded by 0 <= var <= 1

Optimal value: 0 (achived in a=b=c=d=e=f=0)

BARON | Direct | intsolver | interalg | |
---|---|---|---|---|

Elapsed Time, sec | 1000 | 475 | 0.1 | 29 |

Objective value | 0.11 | 0.38 | F | 8.9*10^{-10} |

Source and log | >>> | >>> | >>> | >>> |

BTW, interalg works even with replacing 10^{-15} by 10^{-300} while BARON fails with 10^{-16}

## Test 3

cos(10x_{1}) + (x_{1}-0.01)^{2} + cos(20x_{2}) + (x_{2}-0.02)^{2} + ... + cos(70x_{7}) + (x_{7}-0.07)^{2} -> min

Required accuracy: 10^{-2}

All variables are bounded by 0 <= var <= 1

BARON | Direct | intsolver | interalg | |
---|---|---|---|---|

Elapsed Time, sec | - | >300 | >300 | 27 |

Objective value | - | -6.760 | -6.338 | -6.878 |

Source and log | cannot handle cos |
>>> | >>> | >>> |

# General constrained problems

Despite it is very premature and requires lots of improvements, it is already capable of outperforming commercial BARON and thus can you could be interested in it right now.

## Test 4

This is test 2 (see above) with inequality constraints a*b>0.001, b*c>0.002, c*d>0.003. Tolerances of the constraints have been changed from default 10^{-6} to 10^{-9} (seems like this is default value for BARON)

a / (b + 10^{-15}) + c / (d + 10^{-15}) + e / (f + 10^{-15}) + f / (a + 10^{-15}) + 10^{-7} * (a + b + c + d + e + f)-> min

subjected to

a*b>0.001, b*c>0.002, c*d>0.003

Required accuracy: 10^{-9}

All variables are bounded by 0 <= var <= 1

BARON | interalg | |
---|---|---|

Elapsed Time, sec | >1000 | 4 |

Objective value | 0.11 | 0.0040002006 |

Source and log | >>> | >>> |