206 research outputs found
Distributed Optimization of Clique-Wise Coupled Problems via Three-Operator Splitting
In this study, we explore distributed optimization problems with clique-wise
coupling through the lens of operator splitting. This framework of clique-wise
coupling extends beyond conventional pairwise coupled problems, encompassing
consensus optimization and formation control, and is applicable to a wide array
of examples. We first introduce a matrix, called the clique-wise duplication
(CD) matrix, which enables decoupled reformulations for operator splitting
methods and distributed computation. Leveraging this matrix, we propose a new
distributed optimization algorithm via Davis-Yin splitting (DYS), a versatile
three-operator splitting method. We then delve into the properties of this
method and demonstrate how existing consensus optimization methods (NIDS, Exact
Diffusion, and Diffusion) can be derived from our proposed method. Furthermore,
being inspired by this observation, we derive a Diffusion-like method, the
clique-based projected gradient descent (CPGD), and present Nesterov's
acceleration and in-depth convergence analysis for various step sizes. The
paper concludes with numerical examples that underscore the efficacy of our
proposed method.Comment: 16page
Distributed Optimization of Clique-wise Coupled Problems
This study addresses a distributed optimization with a novel class of
coupling of variables, called clique-wise coupling.
A clique is a node set of a complete subgraph of an undirected graph.
This setup is an extension of pairwise coupled optimization problems (e.g.,
consensus optimization) and allows us to handle coupling of variables
consisting of more than two agents systematically.
To solve this problem, we propose a clique-based linearized ADMM algorithm,
which is proved to be distributed.
Additionally, we consider objective functions given as a sum of nonsmooth and
smooth convex functions and present a more flexible algorithm based on the
FLiP-ADMM algorithm.
Moreover, we provide convergence theorems of these algorithms.
Notably, all the algorithmic parameters and the derived condition in the
theorems depend only on local information, which means that each agent can
choose the parameters in a distributed manner.
Finally, we apply the proposed methods to a consensus optimization problem
and demonstrate their effectiveness via numerical experiments
Gradient-Based Distributed Controller Design Over Directed Networks
In this study, we propose a design methodology of distributed controllers for
multi-agent systems on a class of directed interaction networks by extending
the gradient-flow method. Although the gradient-flow method is a common design
tool for distributed controllers, it is inapplicable to directed networks.
First, we demonstrate how to construct a distributed controller for systems
over a class of time-invariant directed graphs. Subsequently, we achieve better
convergence properties and performance enhancement than the conventional
gradient-flow method. To illustrate its application in time-varying networks,
we address the dynamic matching problem of two distinct groups of agents with
different sensing ranges. This problem is a novel coordination task that
involves pairing agents from two distinct groups to achieve a convergence of
the paired agents' states to the same value. Accordingly, we apply the proposed
method to this problem and provide sufficient conditions for successful
matching. Lastly, numerical examples for systems on both time-invariant and
time-varying networks demonstrate the effectiveness of the proposed method
Sign change in c-axis thermal expansion and lattice collapse by Ni substitution in Co1-xNixZr2 superconductors
We investigated the structural, electronic, and superconducting properties of
Co1-xNixZr2, in which c-axis thermal expansion is systematically controlled. At
x (smaller than) 0.3, c-axis negative thermal expansion (NTE) was observed, and
the thermal expansion constant {\alpha}c approached zero with increasing x. At
x = 0.4-0.6, zero thermal expansion was observed, and positive thermal
expansion (PTE) appeared for x (greater than) 0.7. By analyzing the c/a ratio,
we observed a possible collapsed transition in the tetragonal lattice at around
x = 0.6-0.8. The lattice collapse results in c-axis PTE and the suppression of
bulk superconductivity.Comment: 16 pages, 5 figures, 1 table, Supporting material
Alteration Reaction and Mass Transfer via Fluids with Progress of Fracturing along the Median Tectonic Line, Mie Prefecture, Southwest Japan
We have analyzed mass transfer in the cataclasite samples collected from the Median Tectonic Line, southwest Japan, in which the degree of fracturing is well correlated with the bulk rock chemical compositions determined by the X-ray fluorescence (XRF) analysis. The results of āisoconā analysis indicate not only a large volume increase up to 110% but also the two-stage mass transfer during cataclasis. At the first stage from the very weakly to weakly fractured rocks, the weight percents of SiO2, Na2O, and K2O increase, while those of TiO2, FeO, MnO, MgO, and CaO decrease. At the second stage from the weakly to moderately and strongly fractured rocks, the trend of mass transfer is reversed. The principal component analysis reveals that the variation of chemical compositions in the cataclasite samples can be mostly interpreted by the mass transfer via fluids and by the difference in chemical composition in the protolith rocks to lesser degree. Finally, the changes in the modal composition of minerals with increasing cataclasis analyzed by the X-ray diffraction (XRD) with the aid of āRockJockā software clearly elucidate that the mass transfer of chemical elements was caused by dissolution and precipitation of minerals via fluids in the cataclasite samples
knn-seq: Efficient, Extensible kNN-MT Framework
k-nearest-neighbor machine translation (kNN-MT) boosts the translation
quality of a pre-trained neural machine translation (NMT) model by utilizing
translation examples during decoding. Translation examples are stored in a
vector database, called a datastore, which contains one entry for each target
token from the parallel data it is made from. Due to its size, it is
computationally expensive both to construct and to retrieve examples from the
datastore. In this paper, we present an efficient and extensible kNN-MT
framework, knn-seq, for researchers and developers that is carefully designed
to run efficiently, even with a billion-scale large datastore. knn-seq is
developed as a plug-in on fairseq and easy to switch models and kNN indexes.
Experimental results show that our implemented kNN-MT achieves a comparable
gain to the original kNN-MT, and the billion-scale datastore construction took
2.21 hours in the WMT'19 German-to-English translation task. We publish our
knn-seq as an MIT-licensed open-source project and the code is available on
https://github.com/naist-nlp/knn-seq . The demo video is available on
https://youtu.be/zTDzEOq80m0
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