Optimal fine of wastewater outfall problem in shallow body of water : A bilevel optimization approach

Abstract

A large literature on bilevel programming has emerged, focussing on optimality conditions of algorithms and theory associated with certain class of problems. The topic treated in this thesis aim to model the wastewater management problems as a bilevel optimization problems and develop algorithms and discretization techniques that deal with the behaviour of the nonlinear wastewater dispersion that is governed by the Navier-Stokes equation. To find the optimal penalty function we construct the emission concentration system solution and define the wastewater management problems as bilevel optimization problems and provide theoretical insight when the problem is reformulated to a single-level formulation using a Karush-Kuhn-Tucker condition approach; then we develop algorithms that allow finding numerical solutions of the wastewater management problems.