set exp /1*20/
    quantities /dZ1,dZ2,dZ3,Z1,Z2,Z3/;

variables dZ1_mod, dZ2_mod, dZ3_mod, P1, P2, P3, P4, w;

table meas(exp,quantities)
         dZ1            dZ2           dZ3           Z1            Z2            Z3
1        -3.1201        1.2452        1.8749        0.8241        0.0938        0.0821
2        -2.4704        0.6498        1.8206        0.6852        0.1345        0.1802
3        -1.9661        0.5061        1.4601        0.5747        0.1654        0.2599
4        -1.5664        0.4316        1.1348        0.4867        0.1899        0.3233
5        -1.2477        0.3517        0.8959        0.4167        0.2095        0.3739
6        -0.9935        0.2795        0.714         0.3609        0.225         0.4141
7        -0.7912        0.222         0.5692        0.3164        0.2374        0.4462
8        -0.63          0.1769        0.4531        0.2811        0.2472        0.4717
9        -0.5017        0.1413        0.3604        0.2529        0.2551        0.492
10       -0.3994        0.1128        0.2866        0.2305        0.2613        0.5082
11       -0.318         0.0901        0.2279        0.2126        0.2663        0.5211
12       -0.2532        0.0721        0.1811        0.1984        0.2702        0.5314
13       -0.2017        0.0577        0.144         0.1871        0.2734        0.5395
14       -0.1607        0.0463        0.1144        0.1781        0.2759        0.546
15       -0.128         0.0374        0.0907        0.1709        0.2779        0.5512
16       -0.102         0.0304        0.0716        0.1652        0.2795        0.5553
17       -0.0812        0.0244        0.0568        0.1606        0.2808        0.5586
18       -0.0639        0.013         0.0509        0.157         0.2818        0.5612
19       -0.0506        0.0076        0.0429        0.1541        0.2826        0.5633
20       -0.0426        0.0254        0.0172        0.1518        0.2832        0.5649
;

equations E1, E2, E3, obj;

E1(exp)..  dZ1_mod(exp) =E=  -P1*meas(exp, 'Z1') +  P2*meas(exp, 'Z2') ;
E2(exp)..  dZ2_mod(exp) =E=  P1*meas(exp, 'Z1') - (P2+P3)*meas(exp, 'Z2')  +  P4*meas(exp, 'Z3') ;
E3(exp)..  dZ3_mod(exp) =E=  P3*meas(exp, 'Z2') -  P4*meas(exp, 'Z3') ;

Obj..  w =E= sum( exp, (dZ1_mod(exp) - meas(exp, 'dZ1'))*(dZ1_mod(exp) - meas(exp, 'dZ1')) + (dZ2_mod(exp) - meas(exp, 'dZ2'))*(dZ2_mod(exp) - meas(exp, 'dZ2')) + (dZ3_mod(exp) - meas(exp, 'dZ3'))*(dZ3_mod(exp) - meas(exp, 'dZ3')) );

P1.lo = 0;
P1.up = 10;
P2.lo = 0;
P2.up = 10;
P3.lo = 10;
P3.up = 50;
P4.lo = 10;
P4.up = 50;

 MODEL TEST / E1, E2, E3, obj / ;

 OPTION LIMROW = 0.0;
 OPTION LIMCOL = 0.0;
*OPTION MINLP=SBB;

 SOLVE TEST USING NLP minimiZING w;