In this article, we propose a numerical algorithm achieving dynamic optimization of a class of processes with input-dependent hydraulic delays. Such delays are often observed in process industries. We use the stationarity conditions to derive an iterative algorithm approaching the solution of this problem by solving a series of simpler auxiliary instances. Interestingly, the algorithm is able to leverage state-of-the-art numerical optimization tools such as IPOPT. The proof of convergence is sketched, highlighting the relevance of the chosen algorithmic structure as a form of gradient descent in a functional space. The practical interest of the algorithm is evidenced using two numerical examples to show its desirable properties of convergence and numerical efficiency. (C) 2019 Elsevier Ltd. All rights reserved.