Local linear convergence analysis of Primal–Dual splitting methods

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.     

The High Energy X-ray telescope (HE) onboard the Insight-HXMT astronomy satellite

The Insight-Hard X-ray Modulation Telescope(Insight-HXMT) is a broadband X-ray and γ-ray(1-3000 ke V) astronomy satellite. One of its three main telescopes is the High Energy X-ray telescope(HE). The main detector plane of HE comprises 18 Na I(Tl)/Cs I(Na) phoswich detectors, where Na I(Tl) is used as the primary detector to measure ~ 20-250 ke V photons incident from the field of view(FOV) defined by collimators, and Cs I(Na) is used as the active shielding detector to Na I(Tl) by pulse shape discrimination. Additionally, Cs I(Na) is used as an omnidirectional γ-ray monitor. The HE collimators have a diverse FOV,i.e. 1.1°×5.7°(15 units), 5.7°×5.7°(2 units), and blocked(1 unit). Therefore, the combined FOV of HE is approximately5.7°×5.7°. Each HE detector has a diameter of 190 mm resulting in a total geometrical area of approximately 5100 cm2, and the energy resolution is ~15% at 60 ke V. For each recorded X-ray event by HE, the timing accuracy is less than 10 μs and the deadtime is less than 10 μs. HE is used for observing spectra and temporal variability of X-ray sources in the 20-250 ke V band either by pointing observations for known sources or scanning observations to unveil new sources. Additionally, HE is used for monitoring the γ-ray burst in 0.2-3 Me V band. This paper not only presents the design and performance of HE instruments but also reports results of the on-ground calibration experiments.     

Syntheses,Characterization, and Luminescence Properties of Three Coordination Complexes with Sulfonate-Phenol Anions and Trivalent Metal Ions

Russian Journal of General Chemistry - A dinuclear Tb complex, Tb2(H2L)3(phen)2 (1), and two similar N-donor coordination complexes, Fe(phen)3·HL (2), Fe(bipy)3·HL·5H2O (3) (Na2H2L =...     

p-Adic函数空间上Hardy型算子的多线性交换子估计

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.     

Random copolymerization of macromonomers as a versatile strategy to synthesize mixed-graft block copolymers

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.