53 research outputs found
Going for broke: a multiple case study of brokerage in education
Although the central role of educational intermediaries that can connect research and practice is increasingly appreciated, our present understanding of their motivations, products, and processes is inadequate. In response, this multiple-case study asks how and why three large-scale intermediaries—Edutopia, the Marshall Memo, and Usable Knowledge—are engaging in brokerage activities, and compares the features of the knowledge they seek to share and mobilize. These entities were deliberately chosen and anticipated to reveal diversity. Multiple data sources were analyzed based primarily upon Ward’s knowledge mobilization framework. These entities contrasted widely, especially in relation to core knowledge dimensions, enabling us to identify two distinct brokerage types. To conclude, theoretical (how to conceptualize brokerage) and practical (how to foster interactive knowledge exchange) implications are presented. This study also reveals certain innovative mobilization approaches, including skillful use of social media and the production of videos depicting how and why to adopt particular strategies
Generalized Forward-Backward Splitting
This paper introduces the generalized forward-backward splitting algorithm
for minimizing convex functions of the form , where
has a Lipschitz-continuous gradient and the 's are simple in the sense
that their Moreau proximity operators are easy to compute. While the
forward-backward algorithm cannot deal with more than non-smooth
function, our method generalizes it to the case of arbitrary . Our method
makes an explicit use of the regularity of in the forward step, and the
proximity operators of the 's are applied in parallel in the backward
step. This allows the generalized forward backward to efficiently address an
important class of convex problems. We prove its convergence in infinite
dimension, and its robustness to errors on the computation of the proximity
operators and of the gradient of . Examples on inverse problems in imaging
demonstrate the advantage of the proposed methods in comparison to other
splitting algorithms.Comment: 24 pages, 4 figure
On the Optimal Linear Convergence Rate of a Generalized Proximal Point Algorithm
The proximal point algorithm (PPA) has been well studied in the literature.
In particular, its linear convergence rate has been studied by Rockafellar in
1976 under certain condition. We consider a generalized PPA in the generic
setting of finding a zero point of a maximal monotone operator, and show that
the condition proposed by Rockafellar can also sufficiently ensure the linear
convergence rate for this generalized PPA. Indeed we show that these linear
convergence rates are optimal. Both the exact and inexact versions of this
generalized PPA are discussed. The motivation to consider this generalized PPA
is that it includes as special cases the relaxed versions of some splitting
methods that are originated from PPA. Thus, linear convergence results of this
generalized PPA can be used to better understand the convergence of some widely
used algorithms in the literature. We focus on the particular convex
minimization context and specify Rockafellar's condition to see how to ensure
the linear convergence rate for some efficient numerical schemes, including the
classical augmented Lagrangian method proposed by Hensen and Powell in 1969 and
its relaxed version, the original alternating direction method of multipliers
(ADMM) by Glowinski and Marrocco in 1975 and its relaxed version (i.e., the
generalized ADMM by Eckstein and Bertsekas in 1992). Some refined conditions
weaker than existing ones are proposed in these particular contexts.Comment: 22 pages, 1 figur
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