Optimal Control of Nonlinear Groundwater Hydraulics: Theoretical Development and Numerical Experiments

Nonlinear optimization models are presented for the optimal operation of an unconfined aquifer system. The aquifer's response equations are developed using finite difference methods, quasilinearization, and matrix calculus. The optimization model, which is structured as a discrete time optimal control problem, identifies the optimal pumping pattern necessary to satisfy an exogenous water demand. A quasilinearization optimization algorithm and projected Lagrangian methods are used for the solution of the planning model. Example problems are presented which demonstrate the viability of the approach for nonlinear, nonconvex groundwater management problems.