@article{1083.49023,
author="Hinterm\"uller, M. and Kovtunenko, V. and Kunisch, K.",
title="{Semismooth Newton methods for a class of unilaterally constrained
variational problems.}",
language="English",
journal="Adv. Math. Sci. Appl. ",
volume="14",
number="2",
pages="513-535",
year="2004",
abstract="{Summary: A class of semismooth Newton methods for quadratic
minimization problems subject to non-negativity constraints resulting from
discretizing classes of optimization problems in function spaces is
considered. For the algorithm, which is equivalent to a primal-dual active
set strategy, locally superlinear as well as global convergence results are
established. The global convergence assertions rely on matrix properties
which characterize classes of discretized differential operators. Further,
under an M-matrix property monotonous convergence with respect to the
constrained components of the primal iterates is established. A
comprehensive report on numerical tests is provided for the scalar-valued
problem with a boundary obstacle, the vector-valued Signorini problem with
an obstacle, and the symmetric crack problem. The numerical results support
the theoretical findings.}",
keywords="{semismooth Newton methods; Lam\'e system; vector-valued Signorini
problem; symmetric crack problem}",
classmath="{*49M25 (Finite difference methods)
90C20 (Quadratic programming)
65K10 (Optimization techniques (numerical methods))
74R10 (Brittle fracture)
}",
}