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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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This study compares the physicochemical properties of six electrolytes comprising of three salts: LiFTFSI, NaFTFSI and KFTFSI in two solvent mixtures, the binary (3EC/7EMC) and the ternary (EC/PC/3DMC). The transport properties (conductivity, viscosity) as a function of temperature and concentration were modeled using the extended Jones-Dole-Kaminsky equation, the Arrhenius model, and the Eyring theory of transition state for activated complexes. Results are discussed in terms of ionicity, solvation shell, and cross-interactions between electrolyte components. The application of the six formulated electrolytes in symmetrical activated carbon (AC)//AC supercapacitors (SCs) was characterized by cyclic voltammetry (CV), galvanostatic cycling with potential limitation (GCPL), electrochemical impedance spectroscopy (EIS) and accelerated aging. Results revealed that the geometrical flexibility of the FTFSI anion allows it to access and diffuse easily in AC whereas its counter ions (Li+, Na+ or K+) can remain trapped in porosity. However, this drawback was partially resolved by mixing LiFTFSI and KFTFSI salts in the electrolyte. 相似文献
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Dapeng Liu Binod R. Giri Milán Szőri Béla Viskolcz Et-touhami Es-sebbar Aamir Farooq 《Proceedings of the Combustion Institute》2021,38(1):967-976
NOx mitigation is a central focus of combustion technologies with increasingly stringent emission regulations. NOx can also enhance the autoignition of hydrocarbon fuels and can promote soot oxidation. The reaction between allyl radical (C3H5) and NOx plays an important role in the oxidation kinetics of propene. In this work, we measured the absolute rate coefficients for the redox reaction between C3H5 and NOx over the temperature range of 1000–1252 K and pressure range of 1.5–5.0 bar using a shock tube and UV laser absorption technique. We produced C3H5 by shock heating of C3H5I behind reflected shock waves. Using a Ti:Sapphire laser system with frequency quadrupling, we monitored the kinetics of C3H5 at 220 nm. Unlike low-temperature chemistry, the two target reactions, C3H5 + NO → products (R1) and C3H5 + NO2 → products (R2), exhibited a strong positive temperature dependence for this radical-radical type reaction. However, these reactions did not show any pressure dependence over the pressure range of 1.5–5.0 bar, indicating that the measured rate coefficients are close to the high-pressure limit. The measured values of the rate coefficients resulted in the following Arrhenius expressions (in unit of cm3/molecule/s):To our knowledge, these are the first high-temperature measurements of allyl + NOx reactions. The reported data will be highly useful in understanding the interaction of NOx with resonantly stabilized radicals as well as the mutual sensitization effect of NOx on hydrocarbon fuels. 相似文献