@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)
}",
}