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1.
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
2.
This work is concerned with the extension of the Jacobi spectral Galerkin method to a class of nonlinear fractional pantograph differential equations. First, the fractional differential equation is converted to a nonlinear Volterra integral equation with weakly singular kernel. Second, we analyze the existence and uniqueness of solutions for the obtained integral equation. Then, the Galerkin method is used for solving the equivalent integral equation. The error estimates for the proposed method are also investigated. Finally, illustrative examples are presented to confirm our theoretical analysis. 相似文献
3.
4.
Benni Du 《Molecular physics》2020,118(2)
Kinetics and mechanism of the gas-phase reaction of CH3C(O)OCH(CH3)CH2OCH3 (MPA) with OH radicals in the presence of O2 and NO have been investigated theoretically by performing a high and reliable level of theory, viz., CCSD(T)/6-311?+?G(d,p)//BH&HLYP/6-311++G(d,p)?+?0.9335×ZPE. The calculations predict that the H-abstraction from the ?CH2?O? position of MPA is the most facile channel, which leads to the formation of the corresponding alkoxy radicals CH3C(O)OCH(CH3)C(O ?)HOCH3 under atmospheric conditions. This activated radicals CH3C(O)OCH(CH3)C(O ?)HOCH3 will undergo further rearrangement, fragmentation and oxidative reactions and predominantly leads to the formation of various products (methyl formate HC(O)OCH3 and acetic anhydride CH3C(O)OC(O)CH3). In the presence of water, acetic anhydride can convert into acetic acid CH3C(O)OH via the hydrolysis reaction. The calculated total rate constants over the temperature range 263–372?K are used to derive a negative activation energy (Ea= ?5.88 kJ/mol) and an pre-exponential factor (A?=?1.78×10?12 cm3 molecule?1 s?1). The obtained Arrhenius parameters presented here are in strong agreement with the experimental values. Moreover, the temperature dependence of the total rate constant over a temperature range of 263?1000?K can be described by k?=?5.60 × 10?14×(T/298?K)3.4×exp(1725.7?K/T) cm3 molecule?1 s?1. 相似文献
5.
6.
Yingchun Wu Haipeng Li Xuecheng Wu Gérard Gréhan Lutz Mädler Cyril Crua 《Proceedings of the Combustion Institute》2019,37(3):3211-3218
Droplet evaporation characterization, although of great significance, is still challenging. The recently developed phase rainbow refractometry (PRR) is proposed as an approach to measuring the droplet temperature, size as well as evaporation rate simultaneously, and is applied to a single flowing n-heptane droplet produced by a droplet-on-demand generator. The changes of droplet temperature and evaporation rate after a transient spark heating are reflected in the time-resolved PRR image. Results show that droplet evaporation rate increases with temperature, from ?1.28 m2/s at atmospheric 293 K to a range of (?1.5, ?8) m2/s when heated to (294, 315) K, agreeing well with the Maxwell and Stefan–Fuchs model predictions. Uncertainty analysis suggests that the main source is the indeterminate gradient inside droplet, resulting in an underestimation of droplet temperature and evaporation rate. With the demonstration on simultaneous measurements of droplet refractive index as well as droplet transient and local evaporation rate in this work, PRR is a promising tool to investigate single droplet evaporation in real engine conditions. 相似文献
7.
利用热丝化学气相沉积法(HFCVD)在碳化硅基底上制备金刚石薄膜,采用场发射扫描电子显微镜、拉曼光谱仪、原子力显微镜研究了在不同甲烷浓度条件下制备的金刚石薄膜表面形貌及物相组成,在干摩擦条件下通过往复式摩擦磨损实验测试并计算了已制备金刚石薄膜的摩擦系数和磨损率,结合物相分析及摩擦磨损实验结果分析了甲烷浓度的改变对金刚石薄膜摩擦磨损性能的影响。结果表明,由于甲烷气体含量的升高,金刚石薄膜结晶质量下降,薄膜由微米晶向纳米晶转变。摩擦磨损实验结果显示:3%甲烷浓度条件下制备的金刚石薄膜耐磨性较好,磨损率为2.2×10-7 mm3/mN;5%甲烷浓度条件下制备的金刚石薄膜摩擦系数最低(0.032),磨损率为5.7×10-7 mm3/mN,制备的金刚石薄膜的耐磨损性能相比于碳化硅基底(磨损率为9.89×10-5 mm3/mN)提升了两个数量级,显著提高了碳化硅基底的耐磨性。 相似文献
8.
《Physics letters. A》2019,383(17):2090-2092
In this paper, we have used Monte Carlo (MC) method to simulate and study the temperature and doping effects on the electric conductivity of fullerene (C60). The results show that the band gap has reduced by the doping and the charge carrier transport is facilitated from valence band to conduction band by the temperature where is touched a 300 K. In this case, the conductivity reached a value of . The electric conductivity of C60 can increase by the triphenylmethane dye crystal violet (CV) alkali metal to reach at 303 K. Our results of MC simulation have a good agreement with those extracted from literature [10], [33]. 相似文献
9.
非线性互补问题的一种全局收敛的显式光滑Newton方法 总被引:2,自引:0,他引:2
本针对Po函数非线性互补问题,给出了一种显式光滑Newton方法,该方法将光滑参数μ进行显式迭代而不依赖于Newton方向的搜索过程,并在适当的假设条件下,证明了算法的全局收敛性。 相似文献
10.
Lu Chuanrong 《数学年刊B辑(英文版)》1997,18(1):71-78
Let $\{\xi_{\bold t}, {\bold t}
\in {\bold Z}^d\}$ be a nonuniform $\varphi$-mixing strictly stationary
real random field with
$E\xi_{\bold 0}=0, E|\xi_{\bold 0}|^{2+\delta}<\infty$ for some
$0<\delta<1$. A sufficient
condition is given for the sequence of partial sum set-indexed process
$\{Z_n(A),\ A\in \Cal A\}$ to converge to Brownian motion. By a direct
calculation, the author shows
that the result holds for a more general class of set index ${\Cal A}$, where
${\Cal A}$ is assumed only to have the metric entropy exponent $r, 0相似文献