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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.
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
5.
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
6.
杨晓光 《应用数学学报(英文版)》1997,13(4):337-341
1.IntroductionIntillspaperweanalyzetheconvergenceonmultiplicativeiterativealgorithmsfortheIninimizationofadiffcrentiablefunctiondefinedonthepositiveorthantofR".ThealgorithmissllggestedbyEggermolltl'],andisrelatedtotheEM[2](Expextation--Maximization)algoritllnlforPositronemissiontonlography[']andimagereconstructi..14].Wecollsidertheproblenl"linf(x)s.t.x20.Themultiplicativeiterativealgorithmshavethel'orlniforj=l,2,',n,withAhdeterminedthroughalinesearch.Whilelusem[5]establishedanelegantconv… 相似文献
7.
Rafael López 《Annals of Global Analysis and Geometry》1997,15(3):201-210
In this paper we study constant mean curvature compact surfaces with two Jordan curves in parallel planes as boundary and we investigate the point at which the surface inherits the symmetries of its boundary. 相似文献
8.
有势场逆问题的边界元法 总被引:5,自引:0,他引:5
本文给出了位势方程逆问题的一种最小二乘边界元解法。控制方程为Laplace方程,但一部分边界上未给出任何边值,而只在某些内点上给出了势函值。这一问题在数学上属不适定问题,但在一定条件下存在唯一解。本文同时给出了一种估计解的可靠性的方法。数值试验表明,这类逆问题采用边界元法是非常有效的。 相似文献
9.
Lisa Lorentzen 《Numerical Algorithms》1995,10(1):69-111
Over the last 20 years a large number of algorithms has been published to improve the speed and domain of convergence of continued fractions. In this survey we show that these algorithms are strongly related. Actually, they essentially boil down to two main principles.We also prove some results on asymptotic expansions of tail values of limit periodic continued fractions.Dedicated to Luigi Gatteschi on his seventieth birthdayThis research was partially supported by The Norwegian Research Council and by the HMC project ROLLS, under contract CHRX-CT93-0416. 相似文献
10.