Invited Session Mon.3.MA 313

Monday, 15:15 - 16:45 h, Room: MA 313

Cluster 3: Complementarity & variational inequalities [...]

Optimization and equilibrium problems II


Chair: Christian Kanzow and Michael Ulbrich



Monday, 15:15 - 15:40 h, Room: MA 313, Talk 1

Sebastian Albrecht
Inverse optimal control of human locomotion

Coauthors: Stefan Glasauer, Marion Leibold, Michael Ulbrich


The general hypothesis of our approach is that human motions are (approximately) optimal for an unknown cost function subject to the dynamics. Considering tasks where participants walk from a start to an end position and avoid collisions with crossing persons, the human dynamics are modeled macroscopically on a point-mass level. The locomotion problem results in an optimal control problem and in case of a crossing interferer an MPC-like approach seems suitable. The task of inverse optimal control is to find the cost function within a given parametrized family such that the solution of the corresponding optimal control problem approximates the recorded human data best. Our solution approach is based on a discretization of the continuous optimal control problem and on a reformulation of the bilevel problem by replacing the discretized optimal control problem by its KKT-conditions. The resulting mathematical program with complementarity conditions is solved by using a relaxation scheme and applying an interior-point solver. Numerical results for different navigation problems including hard and soft constraints in the optimal control problem are discussed.



Monday, 15:45 - 16:10 h, Room: MA 313, Talk 2

Francisco Facchinei
Solving quasi-variational inequalities via their KKT conditions

Coauthors: Christian Kanzow, Simone Sagratella


We propose to solve a general quasi-variational inequality by using its Karush-Kuhn-Tucker conditions.
To this end we use a globally convergent algorithm based on a potential reduction approach. We establish global convergence results for many interesting instances of quasi-variational inequalities, vastly broadening the class of problems that can be solved with theoretical guarantees.
Our numerical testings are very promising and show the
practical viability of the approach.



Monday, 16:15 - 16:40 h, Room: MA 313, Talk 3

Christian Kanzow
Nash equilibrium multiobjective elliptic control problems

Coauthor: Alfio Borzi


The formulation and the semismooth Newton solution of Nash equilibria
multiobjective elliptic optimal control problems are presented. Existence and
uniqueness of a Nash equilibrium is proved. The corresponding solution is
characterized by an optimality system that is approximated by second-order
finite differences and solved with a semismooth Newton scheme. It is
demonstrated that the numerical solution is second-order accurate and that
the semismooth Newton iteration is globally and locally quadratically
convergent. Results of numerical experiments confirm the theoretical
estimates and show the effectiveness of the proposed computational framework.


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