12 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
Monotone Inclusions, Acceleration and Closed-Loop Control
We propose and analyze a new dynamical system with a closed-loop control law
in a Hilbert space , aiming to shed light on the acceleration
phenomenon for \textit{monotone inclusion} problems, which unifies a broad
class of optimization, saddle point and variational inequality (VI) problems
under a single framework. Given
that is maximal monotone, we propose a closed-loop control system that is
governed by the operator , where a feedback law
is tuned by the resolution of the algebraic equation
for some
. Our first contribution is to prove the existence and uniqueness
of a global solution via the Cauchy-Lipschitz theorem. We present a simple
Lyapunov function for establishing the weak convergence of trajectories via the
Opial lemma and strong convergence results under additional conditions. We then
prove a global ergodic convergence rate of in terms of a gap
function and a global pointwise convergence rate of in terms of a
residue function. Local linear convergence is established in terms of a
distance function under an error bound condition. Further, we provide an
algorithmic framework based on the implicit discretization of our system in a
Euclidean setting, generalizing the large-step HPE framework. Although the
discrete-time analysis is a simplification and generalization of existing
analyses for a bounded domain, it is largely motivated by the above
continuous-time analysis, illustrating the fundamental role that the
closed-loop control plays in acceleration in monotone inclusion. A highlight of
our analysis is a new result concerning -order tensor algorithms for
monotone inclusion problems, complementing the recent analysis for saddle point
and VI problems.Comment: Accepted by Mathematics of Operations Research; 42 Page
Complexity-optimal and Parameter-free First-order Methods for Finding Stationary Points of Composite Optimization Problems
This paper develops and analyzes an accelerated proximal descent method for
finding stationary points of nonconvex composite optimization problems. The
objective function is of the form where is a proper closed convex
function, is a differentiable function on the domain of , and
is Lipschitz continuous on the domain of . The main advantage of this method
is that it is "parameter-free" in the sense that it does not require knowledge
of the Lipschitz constant of or of any global topological properties
of . It is shown that the proposed method can obtain an
-approximate stationary point with iteration complexity bounds
that are optimal, up to logarithmic terms over , in both the
convex and nonconvex settings. Some discussion is also given about how the
proposed method can be leveraged in other existing optimization frameworks,
such as min-max smoothing and penalty frameworks for constrained programming,
to create more specialized parameter-free methods. Finally, numerical
experiments are presented to support the practical viability of the method
International Conference on Continuous Optimization (ICCOPT) 2019 Conference Book
The Sixth International Conference on Continuous Optimization took place on the campus of the Technical University of Berlin, August 3-8, 2019. The ICCOPT is a flagship conference of the Mathematical Optimization Society (MOS), organized every three years. ICCOPT 2019 was hosted by the Weierstrass Institute for Applied Analysis and Stochastics (WIAS) Berlin. It included a Summer School and a Conference with a series of plenary and semi-plenary talks, organized and contributed sessions, and poster sessions.
This book comprises the full conference program. It contains, in particular, the scientific program in survey style as well as with all details, and information on the social program, the venue, special meetings, and more