Jose Mario Martinez

1. Constrained optimization algorithms that do not use derivatives have been a fruitful area of research, driven by their applicability to a wide range of problems in engineering and applied scienc...

The Saint-Venant equations are widely used to model real river flows. Solving these equations requires the use of sophisticated partial differential equation (PDE) solvers. In this paper, it is proposed that, under different conditions on data availability, the solution of the Saint-Venant equations can be represented by feasibility models that depend on a moderate number of parameters. In particular, a new non-rectangular model for the shape of cross sections is proposed. This method can be used under different assumptions on the knowledge of the variables influencing the evolution of the system.

The method of virtual stations, introduced in \cite{bmfork2}, deals with the prediction of river levels by means of polynomial regression models using only elevation data and inflow forecasts. The reliable computation ofvirtual stations requires specific optimization methods. The objective error function is nonsmooth and not definedat points that could, in principle, be visited by standard minimization algorithms. To tackle this situation, a modified form of the Augmented Lagrangian is introduced. Discontinuities of the derivatives are handled by means of approximate minimizations on a sequence of boxes in which the objective function is smooth. Numerical experiments demonstrate the effectiveness of the introduced techniques for river-flow predictions. AMS Subject Classification: 90C30, 65K05, 90C90.