Methodes de Decomposition pour la Minimisation d’une Fonction sur un Espace Produit

Martinet, B.; Auslender, Alfred

doi:10.1137/0312047

Cited by 9 publications

(1 citation statement)

References 5 publications

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“…There exist many situations ([11- [3], [5], [8], [10], [12]- [16]) in which the solution set D (P) (assumed to be in E' for simplicity's sake) of a problem P may be expressed as the intersection of the solution sets D (I',) of a finite number of problems Pj, j = 1, 2,..,p, that is D(P)= D(P 1 )In D(P 2 )In .. nD (Pp). In that case, one may try to find a set T, point-to-set maps Aj (.…”

Section: Inroductionmentioning

confidence: 99%

Convergence of relaxation algorithms by averaging

Meyer

1988

Mathematical Programming

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Adaptive relaxation algorithms use anti-jamming schemes that require either a large amount of computation or a large amount of memory.ot this paper~ present5 a non-adaptive approach that possesses substantial computational and memory advantages over the adaptive schemes. The approach uses averaging and may be applied whenever the relaxation algorithm's point-to-set maps satisfy appropriate assumptions.IDWYRIBUtMON ST&TEMEI 3 ._A

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Section: Inroductionmentioning

confidence: 99%

Convergence of relaxation algorithms by averaging

Meyer

1988

Mathematical Programming

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Asymptotic properties of the fenchel dual functional and applications to decomposition problems

Auslender

1992

J Optim Theory Appl

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Solution of symmetric linear complementarity problems by iterative methods

Mangasarian

1977

J Optim Theory Appl

291

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Abstract.A unified treatment is given for iterative algorithms for the solution of the symmetric linear complementarity problem:where M is a given n × n symmetric real matrix and q is a given n × 1 vector. A general algorithm is proposed in which relaxation may be performed both before and after projection on the nonnegative orthant. The algorithm includes, as special cases, extensions of the Jacobi, Gauss-Seidel, and nonsymmetric and symmetric successive overrelaxation methods for solving the symmetric linear complementarity problem. It is shown first that any accumulation point of the iterates generated by the general algorithm solves the linear complementarity problem. It is then shown that a class of matrices, for which the existence of an accumulation point that solves the linear complementarity problem is guaranteed, includes symmetric copositive plus matrices which satisfy a qualification of the type:for some x in R n.Also included are symmetric positive-semidefinite matrices satisfying this qualification, symmetric, strictly copositive matrices, and symmetric positive matrices. Furthermore, when M is symmetric, copositive plus, and has nonzero principal subdeterminants, it is shown that the entire sequence of iterates converges to a solution of the linear complementarity problem.

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Methodes de Decomposition pour la Minimisation d’une Fonction sur un Espace Produit

Cited by 9 publications

References 5 publications

Convergence of relaxation algorithms by averaging

Convergence of relaxation algorithms by averaging

Asymptotic properties of the fenchel dual functional and applications to decomposition problems

Solution of symmetric linear complementarity problems by iterative methods

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