We propose an algorithm for dynamic optimization problems with inequality path constraints. It solves a sequence of approximated problems where the path constraint is imposed on a finite number of points. Between adjacent points, an approximating polynomial of the constraint value is calculated and an additional constraint is imposed on the maximum value of this polynomial. We consider Taylor and Hermite polynomials. New points are added based on constraint violations or large approximations errors of the approximating polynomials. We prove finite convergence to a feasible point assuming: (i) the dynamic optimization problem has a Slater point, (ii) pointwise constraints are respected at each iteration. We compare the performance of the algorithm with the algorithm by Fu et at. (Automatica 62, 2015, p.184-192) for three small case studies and an up-to-date industrial application where we calculate optimal feed rates for a semi-batch emulsion polymerization reactor. The results show that our proposed algorithm needs to solve fewer subproblems, i.e. fewer iterations, at the cost of more constraints, resulting in smaller CPU times.

我们提出了一种针对路径不等式的动态优化问题的算法。它解决了一系列近似问题，其中路径约束施加在有限数量的点上。在相邻点之间，计算约束值的近似多项式，并将附加约束施加于该多项式的最大值。我们考虑泰勒和埃尔米特多项式。基于约束违例或近似多项式的较大近似误差添加新点。我们假设以下条件证明收敛到一个可行点：（i）动态优化问题具有一个Slater点，（ii）在每次迭代中都遵循点状约束。我们将算法的性能与Fu等人的算法进行比较。（Automatica 62，2015，p。184-192）进行了三个小案例研究和最新的工业应用，其中我们计算了半间歇乳液聚合反应器的最佳进料速率。结果表明，我们提出的算法需要解决更少的子问题，即更少的迭代，但代价是更多的约束，从而缩短了CPU时间。