Verification of Real-Time Optimization for Multi-Stage Spray Dryer Operation with Polynomial Optimization

Using polynomial optimization, we demonstrate computationally that the local optima determined by a Newton method (interior-point algorithm) for real-time optimization of multi-stage spray dryer operation are identical to the global optimum. In the first major step, we transform the optimization problem for the multi-stage spray dryer operation into a polynomial optimization problem. In this form, the global optimum can be computed by polynomial optimization. In the second major step, we compare the global optimum with the potential local optima obtained by a Newton method for three operational points of a pilot-size plant and for one operational point of an industrial plant. For each case, the Newton method is initialized at 10,000 different initial points. All the computed potential local optima computed by the Newton method are identical to the global optima computed by polynomial optimization. Consequently, based on this extensive computational evidence, we conclude that the Newton method converges to the global optima for the multi-stage spray dryer real-time optimization problem.