University of Guilan Journal of Mathematical Modeling 2345-394X 14 2 2026 05 01 A gradient projection method for solving nonlinear optimal control problems with time-varying delays 363 378 9002 10.22124/jmm.2025.30121.2691 EN Seyed Mojtaba Meshkani Department of Mathematics, Payame Noor University, 19395-4697, Tehran, Iran Sohrab Effati Department of Applied Mathematics, Faculty of Mathematical Science, Ferdowsi University of Mashhad, Mashhad, Iran Aghileh Heydari Department of Mathematics, Payame Noor University, 19395-4697, Tehran, Iran Journal Article 2025 04 05 An effective numerical method using gradient projection is proposed for solving an optimal control problems that involve time-varying delays in control and state variables. First, a variational inequality is established as necessary conditions. The main idea in variational inequality is to compute the gradient of the objective functional, taking into account time-dependent delays in control and state variables. Then, an iterative scheme utilizing a projection operator is presented, followed by a convergence analysis of the method for a coercive objective functional. At the end, several examples are provided to illustrate that the theoretical finding is efficient. https://jmm.guilan.ac.ir/article_9002_88fdaf2f039648457e05a8b34416b31d.pdf