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31.
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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Youchao Wang Na Tian Weize Sun Boerhan Rena Xusheng Guo Yang Feng Chao Li Xuesong Wang Qianxiong Zhou 《Particle & Particle Systems Characterization》2020,37(5):2000045
Photoactivated chemotherapy (PACT) has appealing merits over traditional chemotherapy as well as photodynamic therapy (PDT) by virtue of its spatial and temporal control on drug activity and oxygen-independent mechanisms of action. However, the short photoactivation wavelengths, e.g., visible light–activated Ru(II)-based PACT agents, limit the clinical application severely. In this work, a facile construction of supramolecular nanoparticles from a poly(ethylene glycol) (PEG)-modified [Ru(dip)2(py-SO3)]+ (abbreviated as Ru-PEG, dip = 4,7-diphenyl-1,10-phenanthroline, py-SO3 = pyridine-2-sulfonate) and 1,3-phenylenebis(pyren-1-ylmethanone) (BP) is shown. While Ru-PEG may undergo photoinduced ligand dissociation and release anticancer species of [Ru(dip)2(H2O)2]2+, BP has extremely large two-photon absorption cross sections (δ2) in the NIR region and intense fluorescence over the wavelengths where Ru-PEG has strong absorption. Thus, two-photon excitation of BP followed by an efficient Förster resonance energy transfer (FRET) from BP to Ru-PEG may lead to a potent inactivation against cisplatin-resistant cancer cells and 3D multicellular tumor spheroids (MCTSs). The residue fluorescence of BP also allows the cellular uptake of the particles to be visualized. This work provides a universal and convenient strategy to realize theranostic PACT in the ideal phototherapeutic window of 650–900 nm. 相似文献
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Nonlinear Dynamics - Oblique collisions are more likely to happen in the realistic translational joint with clearance, compared to the full front impacts. It can be a quite demanding task to... 相似文献
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Crystallography Reports - A cobalt coordination polymer, {[Co(L1)2(H2O)2] · (HCOO)2 · H2O}n, where L1 is a bis(4-(1H-imidazol-1-yl)phenyl)methanone, has been synthesized and characterized... 相似文献
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Sun Yuan Luo Shunlong Lei Xiangyun 《International Journal of Theoretical Physics》2021,60(9):3211-3224
International Journal of Theoretical Physics - Gram matrices arise naturally in the consideration of pair-wise overlap of a family of vectors or quantum pure states, and play an important role in... 相似文献
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Si-Yang Feng Tao Zheng Ai-Jing Sun Zuo-Xiang Wang 《Molecular Crystals and Liquid Crystals》2019,692(1):43-52
AbstractComplexes of [CdL2(NO3)2]·1.5H2O and [Ag2(μ-L)2(NO3)2] were synthesized by the reactions of 2-p-methylphenyl-5-(2-pyridyl)-1,3,4-thiadiazole (L) with Cd(NO3)2·4H2O and AgNO3, respectively. Their structures were determined by single crystal X-ray diffraction. The photophysical property and thermal stability were characterized by FT???IR, UV???Vis absorption, fluorescence, and thermogravimetric analysis (TGA). Both complexes belong to the triclinic system with space group p???1. The central metal of [CdL2(NO3)2]·1.5H2O has a distorted octahedral geometry [CdN4O2], while two central Ag(I) atoms of [Ag2(μ-L)2(NO3)2] exhibit distorted tetrahedral geometries [AgN3O]. 相似文献
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在p-adic域上研究分数次Hardy型算子与CMO(Q_p~n)函数生成的多线性交换子,建立了交换子在Lebesgue空间和Herz空间上的有界性.对Hardy算子的多线性交换子也得到了相应的结果. 相似文献