2,752 research outputs found
Gas phase appearance and disappearance as a problem with complementarity constraints
The modeling of migration of hydrogen produced by the corrosion of the
nuclear waste packages in an underground storage including the dissolution of
hydrogen involves a set of nonlinear partial differential equations with
nonlinear complementarity constraints. This article shows how to apply a modern
and efficient solution strategy, the Newton-min method, to this geoscience
problem and investigates its applicability and efficiency. In particular,
numerical experiments show that the Newton-min method is quadratically
convergent for this problem.Comment: Accepted for Publication in Mathematics and Computers in Simulation.
Available online 6 August 2013, Mathematics and Computers in Simulation
(2013
Deflation for semismooth equations
Variational inequalities can in general support distinct solutions. In this
paper we study an algorithm for computing distinct solutions of a variational
inequality, without varying the initial guess supplied to the solver. The
central idea is the combination of a semismooth Newton method with a deflation
operator that eliminates known solutions from consideration. Given one root of
a semismooth residual, deflation constructs a new problem for which a
semismooth Newton method will not converge to the known root, even from the
same initial guess. This enables the discovery of other roots. We prove the
effectiveness of the deflation technique under the same assumptions that
guarantee locally superlinear convergence of a semismooth Newton method. We
demonstrate its utility on various finite- and infinite-dimensional examples
drawn from constrained optimization, game theory, economics and solid
mechanics.Comment: 24 pages, 3 figure
On the finite termination of an entropy function based smoothing Newton method for vertical linear complementarity problems
By using a smooth entropy function to approximate the non-smooth max-type function, a vertical linear complementarity problem (VLCP) can be treated as a family of parameterized smooth equations. A Newton-type method with a testing procedure is proposed to solve such a system. We show that the proposed algorithm finds an exact solution of VLCP in a finite number of iterations, under some conditions milder than those assumed in literature. Some computational results are included to illustrate the potential of this approach.Newton method;Finite termination;Entropy function;Smoothing approximation;Vertical linear complementarity problems
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