Saturday, 16:30 - 18:30 - Room 108

*Stream: Optimal control and applications*

Chair:

- Optimal Control of Convective FitzHugh-Nagumo Equation

We investigate smooth and sparse optimal control problems (ocp) for convective FitzHugh-Nagumo equation with traveling wave solutions in moving excitable media. The cost function includes distributed space-time and terminal targets. The state and adjoint equations are discretized by SIPG-backward Euler methods. Numerical results are presented to control those waves. We show the validity of the second order optimality conditions for the local solutions of ocp for vanishing Tikhonov regularization parameter. We present also results for reduced order ocp with proper orthogonal decomposition.

- Structural Optimization of Variational Inequalities using Phase Field Regularization

The paper is concerned with the structural optimization of elastic bodies in unilateral contact with a given friction. The contact phenomenon is governed by the elliptic variational inequality. The aim of the optimization problem is to find such distribution of the material density function to minimize the normal contact stress. The phase field approach is used to analyze and solve numerically this optimization problem. The original cost functional is regularized using Ginzburg-Landau free energy functional including the surface and bulk energy terms. These terms allow to control global perim

**CANCELED**~~A.M.Lyapunov methodology in Problems of Stability/Optimality for Complex Systems~~

- A bridge between bilevel programs and Nash games

We study connections between bilevel programming problems and Generalized Nash Equilibrium Problems (GNEP). We provide a complete analysis of the relationship between the vertical bilevel problem and the corresponding horizontal one-level GNEP. We define classes of problems for which solutions of the bilevel program can be computed by finding equilibria of the GNEP. We develop a simple method for the solution of our GNEP; we study how it is then possible to recover a solution of the bilevel problem from the computed equilibrium. Numerical tests show the effectiveness of our approach.

- A single-level approach to multi-leader-follower games

Multi-Leader Common-Follower games (MLCF) are a powerful modelling tool to study complex bilevel systems arising for example in electricity markets. Leveraging the optimal value approach, we introduce a Generalized Nash Equilibrium Problem (GNEP) model based on the first order approximation of follower's value function. This single-level GNEP is closely related to the original MLCF. We show that any KKT point of (a suitably perturbed version of the) former problem is critical for (an approximate) MLCF. Moreover, we define wide classes of problems for which the vice-versa holds as well.