Determine the reaction coefficients
in the thermal isometrization of -pinene.
The linear kinetic model [6] is
Our formulation of the -pinene problem
as an optimization problem follows [21,3].
We use a -stage collocation method,
a uniform partition with subintervals of
, and the standard [2, pages 247-249]
basis representation,
Variables | |
Constraints | |
Bounds | 5 |
Linear equality constraints | |
Linear inequality constraints | 0 |
Nonlinear equality constraints | |
Nonlinear inequality constraints | 0 |
Nonzeros in | |
Nonzeros in |
We provide results for the AMPL formulation with in Table 5.2. The initial values for the parameters are . The initial basis parameters are chosen so that the collocation approximation is piecewise constant and interpolates the data. The solution and data are shown in Figure 5.1.
Solver | ||||
LANCELOT | 1426.01 s | 2720.49 s | ||
1.96766e+01 | 1.93937e+01 | |||
violation | 1.87900e-06 | 6.09920e-06 | ||
iterations | 305 | 179 | ||
LOQO | 28.85 s | 6.15 s | 6.77 s | 16.87 s |
1.98715e+01 | 1.98721e+01 | 1.98721e+01 | 1.98721e+01 | |
violation | 1.3e-11 | 2.2e-13 | 7.6e-13 | 8.4e-13 |
iterations | 389 | 32 | 23 | 21 |
MINOS | 1.98 s | 6.74 s | 21.66 s | 194.84 s |
1.98715e+01 | 1.98721e+01 | 1.98721e+01 | 0.00000e+00 | |
violation | 4.2e-13 | 4.4e-13 | 2.3e-12 | 1.7e+04 |
iterations | 7 | 8 | 7 | 49 |
SNOPT | 3.74 s | 13.1 s | 48.91 s | 235.44 s |
1.98715e+01 | 1.98721e+01 | 1.98721e+01 | 1.98721e+01 | |
violation | 3.9e-13 | 4.2e-13 | 6.7e-13 | 5.1e-13 |
iterations | 13 | 18 | 21 | 37 |
Errors or warnings. Timed out. |
LANCELOT stops with the message step got too small, near the solution for . MINOS fails completely on with unbounded (or badly scaled) problem, while SNOPT manages a [p]rimal feasible solution, which could not satisfy dual feasibility for both .