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
Our investigations into the ZnO–TeO2 system have produced a new phase, zinc(II) hexatellurium(IV) tridecaoxide, ZnTe6O13, with trigonal (R) symmetry, synthesized by repeated heating and cooling to a maximum temperature of 1053 K. The asymmetric unit consists of a Zn atom coordinated in a distorted octahedral fashion by two unique tellurium(IV) oxide units that form trigonal–bipyramidal TeO4 and TeO3+1 corner‐ and edge‐shared polyhedra. Except for the Zn and an O atom, which occupy 6c positions, all atoms occupy 18f general positions. 相似文献
Toluene was methylated with methanol and disproportionated using catalysts containing different Pt contents (0.2, 0.4 and 0.6%) supported on H‐ZSM‐5 or H‐mordenite (H‐M) zeolites in a fixed‐bed flow‐reactor operated atmospherically at temperatures of 300–500 °C in a flow of hydrogen. Platinum dispersion in the zeolite supports and acid sites strength distribution were evaluated using hydrogen chemisorption (1:1 stoichiometry) and ammonia temperature programmed desorption (TPD) in a differential scanning calorimeter (DSC). Toluene methylation was much faster on all catalysts than toluene disproportionation (DISP). Both reactions were more accelerated using H‐ZSM‐5 containing catalysts than H‐M containing catalysts. The yield of xylenes, and in particular para‐xylene, was significantly influenced by the yield of trimethylbenzenes (TMBs) in product. The selectivities for para‐, ortho‐ and meta‐xylenes production were found largely dependent on the Pt content in the catalysts, particularly when supported on H‐ZSM5‐zeolite. However, using Pt/H‐M catalysts, these selectivities were not strictly controlled by Pt content in the catalysts. 相似文献
We report a novel, fast, and automatic SPME-based method capable of extracting a small molecule-drug conjugate (SMDC) from biological matrices. Our method relies on the extraction of the drug conjugate followed by direct elution into an electrospray mass spectrometer (ESI-MS) source for qualitative and quantitative analysis. We designed a tool for extracting the targeting head of a recently synthesized SMDC, which includes acetazolamide (AAZ) as high-affinity ligand specific to carbonic anhydrase IX. Specificity of the extraction was achieved through systematic optimization. The design of the extraction tool is based on noncovalent and reversible interaction between AAZ and CAII that is immobilized on the SPME extraction phase. Using this approach, we showed a 330% rise in extracted AAZ signal intensity compared to a control, which was performed in the absence of CAII. A linear dynamic range from 1.2 to 25 μg/ml was found. The limits of detection (LOD) of extracted AAZ from phosphate-buffered saline (PBS) and human plasma were 0.4 and 1.2 μg/ml, respectively. This with a relative standard deviation of less than 14% (n = 40) covers the therapeutic range.
Nitrilimines were prepared from N-arylhydrazono chlorides and reacted with -alanine yielding the corresponding amidrazones, which were treated with 1,1-carbonyldiimidazole in THF affording the hitherto unknown 3-acetyl-1-aryl-1,4,5,6-tetrahydro-1,2,4-triazepin-7-ones. 相似文献
In the presence of triethylamine, 2-mercaptobenzoic acid readily adds onto acylhydrazonoyl chlorides (1a-c) (precursors of the reactive nitrile imine 1,3-dipolar species) to afford good yields of the corresponding 2-[(2-oxo-1-arylhydrazonopropan-1-yl)mercapto]benzoic acids (2a-c). The latter acyclic adducts, in THF in the presence of 1,1'-carbonyldiimidazole, undergo intramolecular cyclization involving the activated carboxy and the enol functionality to deliver the respective 2-(N-arylhydrazono)-3-oxobenzothiophenes (3a-c). In the solid state, the latter compounds adopt the (Z)-geometry around the C=N double bond as evidenced by single crystal X-ray structure determination for 3b. 相似文献
The novel 7-(N-formyl-, 7-(N-acetyl-, and 7-(N-isobutyrylamino)-2-methylquinoline-5,8-diones were synthesized in excellent overall yields in three steps via the nitration of the commercially available 8-hydroxy-2-methylquinoline followed by a reduction-acylation step and then oxidation. Acid hydrolysis of 7-(N-acetylamino)-2-methylquinoline-5,8-dione (14a) afforded the novel 7-aminoquinoline-5,8-dione 7 in excellent yields. Due to our efficient preparation of dione 14a, we now report a short and practical method for the total synthesis of the potent antitumor agent lavendamycin methyl ester (1b) with an excellent overall yield. 相似文献
Summary. Nitrilimines prepared from N-arylhydrazono chlorides reacted with 2-mercaptonicotinic acid yielding the corresponding addition products, 2-[(2-oxo-1-arylhydrazonopropan-1-yl)mercapto] nicotinic acids, which were treated with 1,1-carbonyldiimidazole in THF affording by cyclocondensation the corresponding hitherto unknown 2-arylhydrazono-3-oxothieno[2,3-b]pyridines. 相似文献
We establish a sharp instability theorem for the bound states of lowest energy of the nonlinear Klein-Gordon equation,utt–u+f(u)=0, and the nonlinear Schrödinger equation, –iut–u+f(u)=0.Supported in part by NSF Grants MCS 81-21487 and MCS 82-01599 相似文献