Minimum Function Values

for the Moré et al. Test Set

The Moré et al. test set is defined in The test set consists of 34 distinct functions:
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


Unconstrained Tests

In most cases, the unconstrained minimum function value is zero, except for

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

Bound Constrained Tests

The following set of bounds is defined in (exponents indicate repetition):

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  


The following table gives the global minimum function values of the bound constrained test problems (single precision accuracy), and in the last column the number of bounds active at the global minimizer.

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


Global Optimization
my home page (http://www.mat.univie.ac.at/~neum)

Arnold Neumaier (Arnold.Neumaier@univie.ac.at)