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In this paper, we study the local linear convergence properties of a versatile class of Primal–Dual splitting methods for minimizing composite non-smooth convex optimization problems. Under the assumption that the non-smooth components of the problem are partly smooth relative to smooth manifolds, we present a unified local convergence analysis framework for these methods. More precisely, in our framework, we first show that (i) the sequences generated by Primal–Dual splitting methods identify a pair of primal and dual smooth manifolds in a finite number of iterations, and then (ii) enter a local linear convergence regime, which is characterized based on the structure of the underlying active smooth manifolds. We also show how our results for Primal–Dual splitting can be specialized to cover existing ones on Forward–Backward splitting and Douglas–Rachford splitting/ADMM (alternating direction methods of multipliers). Moreover, based on these obtained local convergence analysis result, several practical acceleration techniques are discussed. To exemplify the usefulness of the obtained result, we consider several concrete numerical experiments arising from fields including signal/image processing, inverse problems and machine learning. The demonstration not only verifies the local linear convergence behaviour of Primal–Dual splitting methods, but also the insights on how to accelerate them in practice. 相似文献
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Polypyrrole Shell@3D‐Ni Metal Core Structured Electrodes for High‐Performance Supercapacitors 下载免费PDF全文
Gao‐Feng Chen Yu‐Zhi Su Pan‐Yong Kuang Zhao‐Qing Liu Dao‐Yi Chen Xu Wu Nan Li Prof. Shi‐Zhang Qiao 《Chemistry (Weinheim an der Bergstrasse, Germany)》2015,21(12):4614-4621
Three‐dimensional (3D) nanometal films serving as current collectors have attracted much interest recently owing to their promising application in high‐performance supercapacitors. In the process of the electrochemical reaction, the 3D structure can provide a short diffusion path for fast ion transport, and the highly conductive nanometal may serve as a backbone for facile electron transfer. In this work, a novel polypyrrole (PPy) shell@3D‐Ni‐core composite is developed to enhance the electrochemical performance of conventional PPy. With the introduction of a Ni metal core, the as‐prepared material exhibits a high specific capacitance (726 F g?1 at a charge/discharge rate of 1 A g?1), good rate capability (a decay of 33 % in Csp with charge/discharge rates increasing from 1 to 20 A g?1), and high cycle stability (only a small decrease of 4.2 % in Csp after 1000 cycles at a scan rate of 100 mV s?1). Furthermore, an aqueous symmetric supercapacitor device is fabricated by using the as‐prepared composite as electrodes; the device demonstrates a high energy density (≈21.2 Wh kg?1) and superior long‐term cycle ability (only 4.4 % and 18.6 % loss in Csp after 2000 and 5000 cycles, respectively). 相似文献
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An N. Le Ruiqi Liang Xiaoyu Ji Xiaowei Fu Mingjiang Zhong 《Journal of polymer science. Part A, Polymer chemistry》2021,59(21):2571-2580
The random copolymerization of norbornene-functionalized macromonomers was explored as a method of synthesizing mixed-graft block copolymers (mGBCPs). The copolymerization kinetics of a model system of polystyrene (PS) and poly(lactic acid) (PLA) macromonomers was first analyzed, revealing a gradient composition of side chains along the mGBCP backbone. The phase separation behavior of mGBCPs with PS and PLA side chains of various backbone lengths and side chain molar ratios was investigated, and increasing the backbone length was found to stabilize the phase-separated nanostructures. The graft architecture was also demonstrated to improve the processability of the mGBCP, compared to a linear counterpart. Investigations of mGBCPs comprised of polydimethylsiloxane and poly(ethylene oxide) side chains exemplified the diverse self-assembled morphologies, including a Frank-Kasper A15 phase, that can be obtained with mGBCPs synthesized by random copolymerization of macromonomers. Lastly, a ternary mGBCP was synthesized by the copolymerization of three macromonomers. 相似文献