Quadratic programming codes

Solve the following problems via a quadratic programming code. 

To solve the problem a sequential quadratic programming code was used in the outer loop of calculations. Inner loops were used to evaluate the physical properties. Forward-finite differences with a step size of h = 10 7 were used as substitute for the derivatives. Equilibrium data were taken from Holland (1963). The results shown in Table E12.1B were essentially the same as those obtained by Sargent and Gaminibandara. 

To solve the alkylation process problem, the code NPSOL, a successive quadratic programming code in MATLAB, was employed. 

The vector x can contain slack variables, so the equality constraints (8.33) may contain some constraints that were originally inequalities but have been converted to equalities by inserting slacks. Codes for quadratic programming allow arbitrary upper and lower bounds on x we assume x>0 only for simplicity. 

OC/DO-problems can be solved very efficiently and reliably by combining the above problem discretization (piecewise control parameterization and multiple shooting state discretization) with a specifically tailored sequential quadratic programming (SQP) algorithm for the solution of the large, but structured NLP problem (2.3). Such a strategy has been implemented in the optimal control code MUSCOD [6, 13]. 

On page 235-241 is the explicit solution used in Excel format to make studies, or mathematical experiments, of any desired and possible nature. The same organization is used here as in previous Excel applications. Column A is the name of the variable, the same as in the FORTRAN program. Column B is the corresponding notation and Column C is the calculation scheme. This holds until line 24. From line 27 the intermediate calculation steps are in coded form. This agrees with the notation used toward the end of the FORTRAN listing. An exception is at the A, B, and C constants for the final quadratic equation. The expression for B was too long that we had to cut it in two. Therefore, after the expression for A, another forD is included that is then included in B. 

---