VeranstaltungsortAlpen-Adria-Universität KlagenfurtI.2.01Veranstalter Institut für MathematikBeschreibungThema: Optimal Control of Phase-Field Fracture EvolutionKurzfassung: Within this talk, we will address optimization problems governed by phase-field fracture/damage processes. The presence of an irreversibility of the fracture growth gives rise to a nonsmooth system of equations. To derive optimality conditions we introduce an additional regularization and show that the resulting optimization problem is well-posed. We will discuss first order necessary optimality conditions and the corresponding constraint qualifications needed. Finally, we will see, that a quadratic approximation to the optimization problem is always solvable. Further, to allow for the analysis of finite dimensional approximations to this problem, we provide a new regularity resulting providing improved differentiability of elliptic systems with non-smooth coefficients. We will finally give an outlook on the resulting discretization error estimates. This is joint work with: Robert Haller-Dintelmann, Hannes Meinlschmidt, Masoumeh Mohammadi, Ira Neitzel, Thomas WickVortragende(r)Winnifried Wollner KontaktSenka Haznadar (senka.haznadar@aau.at)

VeranstaltungsortAlpen-Adria-Universität KlagenfurtI.2.01Veranstalter Institut für MathematikBeschreibungThema: „A polynomial time algorithm for the linearization problem of the QSPP and its applications“Kurzfassung: Given an instance of the quadratic shortest path problem (QSPP) on a digraph G, the linearization problem for the QSPP asks whether there exists an instance of the linear shortest path problem on G such that the associated costs for both problems are equal for every s-t path in G. We prove here that the linearization problem for the QSPP on directed acyclic graphs can be solved in O(nm^3) time, where n is the number of vertices and m is the number of arcs in G. By exploiting this linearization result, we introduce a family of lower bounds for the QSPP on acyclic digraphs. The strongest lower bound from this family of bounds is the optimal solution of a linear programming problem. To the best of our knowledge, this is the first study in which the linearization problem is exploited to compute bounds for the corresponding optimization problem. Numerical results show that our approach provides the best known linear programming bound for the QSPP.Vortragende(r)Hao Hu (Tilburg University)KontaktSenka Haznadar (senka.haznadar@aau.at)