Sums of squares approximations in polynomial optimization: performance analysis and degree bounds
De Monique Laurent
Some advances in numerical algebraic geometry for computing real solutions
De Jon Hauenstein
Apparaît dans la collection : Jean-Morlet Chair 2022: Research School - Domain Decomposition for Optimal Control Problems / Chaire Jean-Morlet 2022 - Ecole - Décomposition des domaines pour des problèmes de contrôle optimal
In the two lectures an introduction to PDE-constrained optimization is given. Exemplary, the techniques are described for linear elliptic and parabolic equations. First-order optimality conditions are derived. Then, these techniques are extended to more difficult problems including inequality constraints and nonlinearities. Furthermore, second-order methods for optimization are explained.