Optimal control theory is a versatile mathematical discipline with applications in many fields. It has gained interest over the last decades mainly because increasing computational power allowed to tackle large and complex real life problems numerically. For offering reliable results, a thorough theoretical analysis of solution algorithms, their convergence properties, and approximation quality is inevitable.
We follow this need and investigate linear quadratic optimal control problems with elliptic partial differential equations. The discretization with hp-finite elements is embedded in both Newton-type and interior point methods. Different efficient strategies are presented and accompanied by new results on regularity, approximation, and convergence theory.