PROB 1 : ROSENBROCK [rose.m] PROB 2 : FREUDENSTEIN AND ROTH [froth.m] PROB 3 : POWELL BADLY SCALED [badscp.m] PROB 4 : BROWN BADLY SCALED [badscb.m] PROB 5 : BEALE [beale.m] PROB 6 : JENRICH AND SAMPSON [jensam.m] PROB 7 : HELICAL VALLEY [helix.m] PROB 8 : BARD [bard.m ] PROB 9 : GAUSSIAN [gauss.m] PROB 10: MEYER [meyer.m] PROB 11: GULF RESEARCH AND DEVELOPMENT [gulf.m ] PROB 12: BOX 3- DIMENSIONAL [box.m ] PROB 13: POWELL SINGULAR [sing.m] PROB 14: WOOD [wood.m] PROB 15: KOWALIK AND OSBOME [kowosb.m] PROB 16: BROWN AND DENNIS [bd.m] PROB 17: OSBORNE 1 [osb1.m] PROB 18: BIGGS [biggs.m] PROB 19: OSBORNE 2 [osb2.m] PROB 20: WATSON [watson.m] PROB 21: EXTENDED RESENBROCK [rosex.m] PROB 22: EXTENDED POWELL SINGULAR [singx.m] PROB 23: PENALTY 1 [pen1] PROB 24: PENALTY 2 [pen2] PROB 25: VARIABLY DIMENSIONAL [vardim.m] PROB 26: TRIGONOMETRIC [trig.m] PROB 27: BROWN ALMOST LINEAR [almost.m] PROB 28: DISCRETE BOUNDARY VALUE [bv.m] PROB 29: DISCRETE INTEGRAL EQUATION [ie.m] PROB 30: BROYDEN TRIDIAGONAL [trid.m] PROB 31: BROYDEN BANDED [band.m] PROB 32: LINEAR - FULL RANK [lin.m] PROB 33: LINEAR - RANK 1 [lin1.m] PROB 34: LINEAR - RANK 1 W/0 COL & ROWS [lin0.m]It is supplemented by a set of standard starting points. Typically, these are scaled by factors 1, 10, and 100 to test the ability of an algorithm to reach the solution from a close, medium apart, and far apart starting point. Fortran Code for Moré/Garbow/Hillstrom (and some other) test functions, gradients, and standard starting points
MATLAB Code for Moré/Garbow/Hillstrom test functions, gradients, and standard starting points
case | minimum function value ------------------------------- 9 | 1.12793 10^-8 16 | 8.58222 10^+4 20 | 2.28767 10^-3 23 | 2.24997 10^-5 24 | 9.37629 10^-6
problem | dim | lower bounds | upper bounds --------------------------------------------------- 7 | 3 | -100,-1,-1 | .8,1,1 18 | 6 | 0^3,1,0,0 | 2,8,1,7,5,5 9 | 3 | .398,1,-.5 | 4.2,2,.1 3 | 2 | 0,1 | 1,9 12 | 3 | 0,5,0 | 2,9.5,20 25 | 10 | 0^10 | 10,20,30,40,50,60,70,80,90,.5 20 | 9 | -.00001,0^4,-3,0,-3,0 | .00001,.9,.1,1,1,0,4,0,2 20 | 12 | -1,0,-1^3,0,-3,0,-10,0,-5,0 | 0,.9,0,.3,0,1,0,10,0,10,0,1 23 | 10 | 0,1,0^3,1,0^3,1 | 100^10 24 | 4 | -10,.3,0,-1 | 50^3,.5 24 | 10 | -10,.1,0,.05,0,-10,0,.2,0,0 | 50^9,.5 4 | 2 | 0,.000 03 | 1 000 000,100 16 | 4 | -10,0,-100,-20 | 100,15,0,.2 11 | 3 | 0^3 | 10^3 26 | 10 | 0,10,20,30,40,50,60,70,80,90 | 10,20,30,40,50,60,70,80,90,100 21 | 2 | -50,0 | .5,100 22 | 4 | .1,-20,-1,-1 | 100,20,1,50 5 | 2 | .6,.5 | 10,100 14 | 4 | -100^4 | 0,10,100,100 35 | 7 | 0^7 | .05,.23,.333,1^4 35 | 8 | 0,0,.1,0^5 | .04,.2,.3,1^5 35 | 9 | 0,0,.1,0^6 | 1,.2,.23,.4,1^5 35 | 10 | 0,.1,.2,0,0,.5^5 | 1,.2,.3,.4,.4,1^5
problem | dim | f_target | act ------------------------------------------ 7 | 3 | 0.99042212 10^-0 | 1 18 | 6 | 0.53209865 10^-3 | 2 9 | 3 | 0.11279300 10^-7 | 1 3 | 2 | 0.15125900 10^-9 | 1 12 | 3 | 0.30998153 10^-5 | 1 25 | 10 | 0.33741268 10^-0 | 1 20 | 9 | 0.37401397 10^-1 | 5 20 | 12 | 0.71642800 10^-1 | 7 23 | 10 | 0.75625699 10^+1 | 10 24 | 4 | 0.94343600 10^-5 | 1 24 | 10 | 0.29442600 10^-3 | 0 4 | 2 | 0.78400000 10^+3 | 2 16 | 4 | 0.88860479 10^+5 | 2 11 | 3 | 0.58281431 10^-4 | 2 26 | 10 | 0.00000000 10^-0 | 0 21 | 2 | 0.25000000 10^-0 | 1 22 | 4 | 0.18781963 10^-3 | 1 5 | 2 | 0.00000000 10^-0 | 1 14 | 4 | 0.15567008 10^+1 | 1 35 | 7 | 0.98323258 10^-3 | 3 35 | 8 | 0.36399851 10^-2 | 1 35 | 9 | 0.10941440 10^-4 | 2 35 | 10 | 0.65039548 10^-2 | 0
Arnold Neumaier (Arnold.Neumaier@univie.ac.at)