This paper focuses on a new approach to describe coastal morphodynamics, based on optimization theory, and more specifically on the assumption that a sandy seabed evolves in order to minimize a wave-related function, the choice of which depends on what is considered the driving force behind coastal morphodynamics. The numerical model derived from this theory uses a gradient descent method and permits to accounts for physical constraints such as sand conservation in basin experiments. Hence, the model automatically adapts to either basin or open sea settings and only involves two hyper-parameters: the sand abrasion and the critical angle of repose. The model behavior is illustrated on a flume configuration. Comparison of the resulting seabed with experimental data as well as with the results of the widely distributed coastal morphodynamic software XBeach demonstrate the potential of a model by wave energy minimization.