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methanol.gms : Methanol to hydrocarbons COPS 2.0 #13

Determine the reaction coefficients for the conversion of methanol
into various hydrocarbons.

This model is from the COPS benchmarking suite.
See http://www-unix.mcs.anl.gov/~more/cops/.

The number of discretization points can be specified using the command
line parameter --nh. COPS performance tests have been reported for nh
= 50, 100, 200, 400
References:
Large Model of Type: NLP    Includes:  copspart.inc
$Title Methanol to hydrocarbons COPS 2.0 #13 (METHANOL,SEQ=241) $ontext Determine the reaction coefficients for the conversion of methanol into various hydrocarbons. This model is from the COPS benchmarking suite. See http://www-unix.mcs.anl.gov/~more/cops/. The number of discretization points can be specified using the command line parameter --nh. COPS performance tests have been reported for nh = 50, 100, 200, 400 Dolan, E D, and More, J J, Benchmarking Optimization Software with COPS. Tech. rep., Mathematics and Computer Science Division, 2000. Tjoa, I B, and Biegler, L T, Simultaneous Solution and Optimization Strategies for Parameter Estimation of Differential-Algebraic Equations Systems. Ind. Eng. Chem. Res. 30 (1991), 376-385. Averick, B M, Carter, R G, More, J J, and Xue, G L, The MINPACK-2 Test Problem Collection. Tech. rep., Mathematics and Computer Science Division, Argonne National Laboratory, 1992. Maria, G, An Adaptive Strategy for Solving Kinetic Model Concomitant Estimation - Reduction Problems. Can. J. Chem. Eng. 67 (1989), 825. Ascher, U M, Mattheij, R M M, and Russell, R D, Numerical Solution of Boundary Value Problems for Ordinary Differential Equations. SIAM, 1995. Floudas, C A, Pardalos, P M, Adjiman, C S, Esposito, W R, Gumus, Z H, Harding, S T, Klepeis, J L, Meyer, C A, and Schweiger, C A, Handbook of Test Problems in Local and Global Optimization. Kluwer Academic Publishers, 1999. $offtext $if set n $set nh %n% $if not set nh $set nh 50 Set ne differential equations /ne1*ne3/ np ODE parameters /np1*np5/ nc collocation points /nc1*nc3/ nh partition intervals /nh1*nh%nh%/ nm measurements /1*17/; Parameter bc(ne) ODE initial conditions / ne1 1, ne2 0, ne3 0/ tau(nm) times at which observations made / 1 0.000, 2 0.050, 3 0.065, 4 0.080, 5 0.123, 6 0.233, 7 0.273, 8 0.354, 9 0.397, 10 0.418, 11 0.502, 12 0.553, 13 0.681, 14 0.750, 15 0.916, 16 0.937, 17 1.122 /; Table z(nm,ne) observation ne1 ne2 ne3 1 1.0000 0 0 2 0.7085 0.1621 0.0811 3 0.5971 0.1855 0.0965 4 0.5537 0.1989 0.1198 5 0.3684 0.2845 0.1535 6 0.1712 0.3491 0.2097 7 0.1198 0.3098 0.2628 8 0.0747 0.3576 0.2467 9 0.0529 0.3347 0.2884 10 0.0415 0.3388 0.2757 11 0.0261 0.3557 0.3167 12 0.0208 0.3483 0.2954 13 0.0085 0.3836 0.2950 14 0.0053 0.3611 0.2937 15 0.0019 0.3609 0.2831 16 0.0018 0.3485 0.2846 17 0.0006 0.3698 0.2899 ; $batinclude copspart.inc nc3 17 Positive variable theta(np) ODE parameters; Equations collocation_eqn1(nh,nc) collocation_eqn2(nh,nc) collocation_eqn3(nh,nc); collocation_eqn1(i,j).. Duc[i,j,'ne1'] =e= - (2*theta['np2'] - (theta['np1']*uc[i,j,'ne2'])/ ((theta['np2']+theta['np5'])*uc[i,j,'ne1']+uc[i,j,'ne2']) + theta['np3'] + theta['np4'])*uc[i,j,'ne1']; collocation_eqn2(i,j).. Duc[i,j,'ne2'] =e= (theta['np1']*uc[i,j,'ne1']*(theta['np2']*uc[i,j,'ne1']-uc[i,j,'ne2']))/ ((theta['np2']+theta['np5'])*uc[i,j,'ne1']+uc[i,j,'ne2']) + theta['np3']*uc[i,j,'ne1']; collocation_eqn3(i,j).. Duc[i,j,'ne3'] =e= (theta['np1']*uc[i,j,'ne1']*(uc[i,j,'ne2']+theta['np5']*uc[i,j,'ne1']))/ ((theta['np2']+theta['np5'])*uc[i,j,'ne1']+uc[i,j,'ne2']) + theta['np4']*uc[i,j,'ne1']; model methanol /all/; theta.l(np) = 1; v.fx['nh1',s] = bc(s); $if set workspace methanol.workspace = %workspace%; solve methanol minimizing obj using nlp;