The talk Nonlinear optimization and hemivariational inequalities for unilateral crack problems, by Victor A. Kovtunenko (Inst. for Math. and Sci. Comp., Univ. of Graz, Austria, and Lavrent ev Inst. of Hydrodynamics, Novosibirsk, Russia), will be held on Monday February 22, 2016 at 9:00 in room K6.
In the nonlinear optimization framework we introduce a class of generalized complementarity problem governing by minimization of non-convex and non-differentiable objective functions. As the result, necessary and sufficient optimality conditions for the minimization problem do not coincide. While the necessary optimality condition is represented as a hemivariational inequality (HemVI), the sufficient optimality condition is expressed as a saddle point problem.
As the reference application, we consider obstacle and crack models due to dissipative contact under cohesion and non-monotone friction phenomena. The nonlinear crack problems belong to the field of quasi-brittle fracture. For engineering applications, to determine stress intensity factors under the nonlinear contact conditions is of primary interest.
From the perspective of numerical optimization, primal-dual active set (PDAS) methods are developed to efficiently compute solutions of the underlying minimization problems. The common advantage of PDAS-methods lies in the fact that they are associated to generalized Newton methods. Locally super-linear und globally monotone convergence properties of our algorithm are established, and comparative numerical tests are presented also for non-unique solutions.