Decomposition through formalization in a product space

Pierra, Guy

doi:10.1007/bf02612715

Cited by 245 publications

(203 citation statements)

References 8 publications

Supporting

Mentioning

199

Contrasting

Unclassified

Order By: Relevance

“…Our approach to the convergence of the method of averaged projections is standard [5,38,39]: we identify the method with von Neumann's alternating projections algorithm [49] on two closed sets (one of which is a linear subspace) in a suitable product space. A nice development of the classical method of alternating projections in the convex case may be found in [15].…”

Section: Introductionmentioning

confidence: 99%

Local Linear Convergence for Alternating and Averaged Nonconvex Projections

2008

View full text Add to dashboard Cite

The idea of a finite collection of closed sets having "linearly regular intersection" at a point is crucial in variational analysis. This central theoretical condition also has striking algorithmic consequences: in the case of two sets, one of which satisfies a further regularity condition (convexity or smoothness for example), we prove that von Neumann's method of "alternating projections" converges locally to a point in the intersection, at a linear rate associated with a modulus of regularity. As a consequence, in the case of several arbitrary closed sets having linearly regular intersection at some point, the method of "averaged projections" converges locally at a linear rate to a point in the intersection. Inexact versions of both algorithms also converge linearly.

show abstract

Section: Introductionmentioning

confidence: 99%

Local Linear Convergence for Alternating and Averaged Nonconvex Projections

2008

View full text Add to dashboard Cite

show abstract

“…This algorithm has been proposed in Pierra [15]. As (17) has a unique optimal solution, from Theorem 1, we conclude that the séquence {x f } converges to a limit point x K and, when A i 0, from Theorem 2, JC A tends to a solution of (15).…”

Section: Application To the Decomposition Of Convex Programsmentioning

confidence: 67%

“…As (17) has a unique optimal solution, from Theorem 1, we conclude that the séquence {x f } converges to a limit point x K and, when A i 0, from Theorem 2, JC A tends to a solution of (15). In practice, we need a test to décide whether we must reduce A and solve another cycle of itérations (17)- (18) or not.…”

Section: Application To the Decomposition Of Convex Programsmentioning

confidence: 92%

“…The ability of dealing with nonsmoothness. The nice effect of the regularization on the decentralization of subproblems in the décomposition of large-scale programs (see [2], [10] and [15]). …”

Section: (X = U N )mentioning

confidence: 99%

“…The itération 1 décomposes in two steps, one proximal itération on ƒ which maintains separability and a projection on C which satisfies the coupling. This idea has been used by Pierra [15] in this context, but the convergence proof we propose hère, beside the fact that it applies to the splitting of gênerai operators, is more straightforward and less restrictive than his proof. …”

Section: (X = U N )mentioning

confidence: 99%

See 2 more Smart Citations

Partial regularization of the sum of two maximal monotone operators

Mahey¹,

Tao²

1993

ESAIM: M2AN

View full text Add to dashboard Cite

The Kabachnik–Fields and Pudovik Reactions on the Basis of E,Z‐Citral and Its Imines and (R,S)‐Citronellal

Низамов¹,

Yambushev

Nizamov

et al. 2012

Heteroatom Chemistry

View full text Add to dashboard Cite

The Kabachnik–Fields reaction of E,Z‐citral with diethyl phosphite in the presence of isobutylamine has been found to form α‐aminophosphonates. The Pudovik reactions of diethyl phosphite with prenyl imines prepared on the basis of E,Z‐citral with isobutylamine also allowed us to obtain the same α‐aminophosphonates. We have managed to synthesize α‐aminophosphonates by the reaction of O,O‐dialkyl trimethylsilyl phosphites with prenyl imines in the presence of water or diethylamine. α‐Aminophosphonates were also synthesized by the reaction of diethyl phosphite with (R,S)‐citronellal in the presence of alkylamines. α‐Aminophosphonates obtained showed bacteriostatic activity against Staphylococcus aureus and Bacillus cereus. © 2012 Wiley Periodicals, Inc. Heteroatom Chem 24:36–42, 2013; View this article online at http://wileyonlinelibrary.com. DOI 10.1002/hc.21060

show abstract

Decomposition through formalization in a product space

Cited by 245 publications

References 8 publications

Local Linear Convergence for Alternating and Averaged Nonconvex Projections

Local Linear Convergence for Alternating and Averaged Nonconvex Projections

Partial regularization of the sum of two maximal monotone operators

The Kabachnik–Fields and Pudovik Reactions on the Basis of E,Z‐Citral and Its Imines and (R,S)‐Citronellal

Contact Info

Product

Resources

About