#************************************************************* # Test Problem 4 from Chapter 11, section 3.6 # Bellman's Problem #************************************************************* OPTION {{ FTOL = 1e-8; OTOL = 1e-8; NLP = "SNOPT"; }} DECLARATION {{ INDEX {m,i,p}; SET M = |1:14|; # Number of Data sets SET I = |1:1|; # Number of Variables SET P = |1:2|; # Number of Parameters XVAR {x(M,I), # Fitted data variables a(P) # Parameters }; ZVAR {z(I)}; ISPE {z(I)}; ZINC {0}; TIME {0,1.0,2.0,3.0,4.0,5.0,6.0,7.0,9.0,11.0,14.0,19.0,24.0,29.0,39.0}; # Observed data PARA xe(M,I) = {1.4,6.3,10.4,14.2,17.6,21.4,23.0,27.0,30.4,34.4, 38.8,41.6,43.5,45.3}; # Variable Bounds LBDS x(M,I) = < m E M | < i E I | xe(m,i) - 5 > >; UBDS x(M,I) = < m E M | < i E I | xe(m,i) + 5 > >; LBDS a(P) = < p E P | 0>; UBDS a(P) = < p E P | 0.1>; }} MODEL {{ MIN: <> >>;1, dae1: z'(1) =e= a(1)*(126.2 - z(1))*(91.9 - z(1))^2 - a(2)*z(1)^2; err(m E M,i E I)[m]: z(i) - x(m,i) =e= 0; }}