402 research outputs found
New Relaxation Modulus Based Iterative Method for Large and Sparse Implicit Complementarity Problem
This article presents a class of new relaxation modulus-based iterative
methods to process the large and sparse implicit complementarity problem (ICP).
Using two positive diagonal matrices, we formulate a fixed-point equation and
prove that it is equivalent to ICP. Also, we provide sufficient convergence
conditions for the proposed methods when the system matrix is a -matrix or
an -matrix.
Keyword: Implicit complementarity problem, -matrix, -matrix, matrix
splitting, convergenceComment: arXiv admin note: substantial text overlap with arXiv:2303.1251
Applications of a splitting algorithm to decomposition in convex programming and variational inequalities
Cover title.Includes bibliographical references.Partially supported by the U.S. Army Research Office (Center for Intelligent Control Systems) DAAL03-86-K-0171 Partially supported by the National Science Foundation. NSF-ECS-8519058by Paul Tseng
On the initial estimate of interface forces in FETI methods
The Balanced Domain Decomposition (BDD) method and the Finite Element Tearing
and Interconnecting (FETI) method are two commonly used non-overlapping domain
decomposition methods. Due to strong theoretical and numerical similarities,
these two methods are generally considered as being equivalently efficient.
However, for some particular cases, such as for structures with strong
heterogeneities, FETI requires a large number of iterations to compute the
solution compared to BDD. In this paper, the origin of the bad efficiency of
FETI in these particular cases is traced back to poor initial estimates of the
interface stresses. To improve the estimation of interface forces a novel
strategy for splitting interface forces between neighboring substructures is
proposed. The additional computational cost incurred is not significant. This
yields a new initialization for the FETI method and restores numerical
efficiency which makes FETI comparable to BDD even for problems where FETI was
performing poorly. Various simple test problems are presented to discuss the
efficiency of the proposed strategy and to illustrate the so-obtained numerical
equivalence between the BDD and FETI solvers
A two-step iteration method for solving vertical nonlinear complementarity problems
In this paper, for vertical nonlinear complementarity problems, a two-step modulus-based matrix splitting iteration method is established by applying the two-step splitting technique to the modulus-based matrix splitting iteration method. The convergence theorems of the proposed method are given when the number of system matrices is larger than 2. Numerical results show that the convergence rate of the proposed method can be accelerated compared to the existing modulus-based matrix splitting iteration method
Further applications of a splitting algorithm to decomposition in variational inequalities and convex programming
Cover title.Includes bibliographical references.Partially supported by the U.S. Army Research Office (Center for Intelligent Control Systems) DAAL03-86-K-0171 Partially supported by the National Science Foundation. NSF-ECS-8519058Paul Tseng
Forward-backward truncated Newton methods for convex composite optimization
This paper proposes two proximal Newton-CG methods for convex nonsmooth
optimization problems in composite form. The algorithms are based on a a
reformulation of the original nonsmooth problem as the unconstrained
minimization of a continuously differentiable function, namely the
forward-backward envelope (FBE). The first algorithm is based on a standard
line search strategy, whereas the second one combines the global efficiency
estimates of the corresponding first-order methods, while achieving fast
asymptotic convergence rates. Furthermore, they are computationally attractive
since each Newton iteration requires the approximate solution of a linear
system of usually small dimension
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