New methods for solving certain types of PDE-constrained optimization problems are presented in this thesis. The approach taken is to augment state-of-the-art PDE methods. The PDE variables and the optimization variables are solved for simultaneously. This impacts the PDE method by changing the core from solving a system of nonlinear equations to that of finding a nonlinear saddle point. This i...

The goal in multiobjective optimization is to determine the so-called Pareto set. Our problem governed by a parameter-dependent semi-linear elliptic partial differential equation (PDE). To solve it, we use gradient-based set-oriented numerical method. solution of PDE standard discretization methods usually leads high computational effort. overcome this difficulty, reduced-order modeling (ROM) d...