A new interior-point boundary projection method for solving nonlinear groundwater pollution control problems

A new interior-point algorithm for solving the groundwater-pollution-control design problem is presented. The algorithm requires that the objective function is differentiable in the interior region. For minimization problems with nonlinear constraints and a concave objective function, the technique is shown to be similar to an active set gradient-projection method, where the tangent of the boundary between feasible and infeasible solutions is used to determine a search direction. In this new method, however, the search direction is translated into the interior space of the feasible region. This process allows progress to be made toward improving the objective function while remaining in the feasible space and ultimately converges to a stationary point. Although the solution technique was developed to solve a groundwater control formulation with a linear objective function and nonlinear constraints, the method has been successfully applied to an unconstrained nonconcave/nonconvex formulation and may be applicable to a wide variety of problems.