1,144 research outputs found
Stability and Error Analysis for Optimization and Generalized Equations
Stability and error analysis remain challenging for problems that lack
regularity properties near solutions, are subject to large perturbations, and
might be infinite dimensional. We consider nonconvex optimization and
generalized equations defined on metric spaces and develop bounds on solution
errors using the truncated Hausdorff distance applied to graphs and epigraphs
of the underlying set-valued mappings and functions. In the process, we extend
the calculus of such distances to cover compositions and other constructions
that arise in nonconvex problems. The results are applied to constrained
problems with feasible sets that might have empty interiors, solution of KKT
systems, and optimality conditions for difference-of-convex functions and
composite functions
Frictional Collisions Off Sharp Objects
This work develops robust contact algorithms capable of dealing with multibody nonsmooth contact
geometries for which neither normals nor gap functions can be defined. Such situations arise
in the early stage of fragmentation when a number of angular fragments undergo complex collision
sequences before eventually scattering. Such situations precludes the application of most contact
algorithms proposed to date
Fast solution of Cahn-Hilliard variational inequalities using implicit time discretization and finite elements
We consider the eļæ½cient solution of the Cahn-Hilliard variational inequality using an implicit time discretization, which is formulated as an optimal control problem with pointwise constraints on the control. By applying a semi-smooth Newton method combined with a Moreau-Yosida regularization technique for handling the control constraints we show superlinear convergence in function space. At the heart of this method lies the solution of large and sparse linear systems for which we propose the use of preconditioned Krylov subspace solvers using an eļæ½ective Schur complement approximation. Numerical results illustrate the competitiveness of this approach
- ā¦