12,432 research outputs found
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
Variational Inequalities in Critical-State Problems
Similar evolutionary variational inequalities appear as convenient
formulations for continuous quasistationary models for sandpile growth,
formation of a network of lakes and rivers, magnetization of type-II
superconductors, and elastoplastic deformations. We outline the main steps of
such models derivation and try to clarify the origin of this similarity. New
dual variational formulations, analogous to mixed variational inequalities in
plasticity, are derived for sandpiles and superconductors.Comment: Submitted for publicatio
Convergence of optimal control problems governed by second kind parabolic variational inequalities
We consider a family of optimal control problems where the control variable
is given by a boundary condition of Neumann type. This family is governed by
parabolic variational inequalities of the second kind. We prove the strong
convergence of the optimal controls and state systems associated to this family
to a similar optimal control problem. This work solves the open problem left by
the authors in IFIP TC7 CSMO2011
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