On Discretize then Optimization Approach of Heat Optimization Problem

Optimization problems which are governed by partial differential equations arise in many applications and are classically solved by ”optimize then discretize” approach. However, recent advances in computing allow us to take an alternative approach of ”discretize then optimize”, which transforms the continuous problem into a standard but large optimization problem. In this poster, the latter approach is studied more closely for ”heat-equation optimization problem”. Different discretization methods and their importance in stability of the problem are discussed. Moreover, two possible models of the problem are considered and their computational efficiency is compared.