This paper is devoted to the theoretical and numerical investigation of an augmented Lagrangian method for the solution of optimization problems with geometric constraints. Specifically, we study situations where parts of the constraints are nonconvex and possibly complicated, but allow for a fast computation of projections onto this nonconvex set. Typical problem classes which satisfy this requirement are optimization problems with disjunctive constraints (like complementarity or cardinality constraints) as well as optimization problems over sets of matrices which have to satisfy additional rank constraints. The key idea behind our method is to keep these complicated constraints explicitly in the constraints and to penalize only the remaining constraints by an augmented Lagrangian function. The resulting subproblems are then solved with the aid of a problem-tailored nonmonotone projected gradient method. The corresponding convergence theory allows for an inexact solution of these subproblems. Nevertheless, the overall algorithm computes so-called Mordukhovich-stationary points of the original problem under a mild asymptotic regularity condition, which is generally weaker than most of the respective available problem-tailored constraint qualifications. Extensive numerical experiments addressing complementarity- and cardinality-constrained optimization problems as well as a semidefinite reformulation of MAXCUT problems visualize the power of our approach.
Polymerizable rare earth complex Eu(AA)3Phen was synthesized by complexion of europium ion, acrylic acid (AA), and 1,10-phenanthroline (Phen). The structure and fluorescence properties of the complex were studied by elemental analysis, 1H-NMR spectroscopy, and fluorescence spectroscopy. Eu-containing copolymer poly(PEGMA-co-MMA-co-METAC-co-Eu(AA)3Phen) (PPMMEu) was then synthesized by free radical copolymerization of Eu(AA)3Phen and other functional monomers including poly(ethylene glycol) methyl ether methacrylate (PEGMA) and [2-(Methacryloyloxy) ethyl] trimethylammonium chloride (METAC). 1H-NMR spectroscopy and fluorescence spectroscopy were used to characterize the copolymer and the interactions between the copolymer and DNA was investigated by TEM, fluorescence spectroscopy, and agarose gel electrophoresis. The desired luminescent cationic copolymer was successfully obtained. The copolymer can form micelles in water solution and can efficiently bind to DNA molecules through electrostatic interaction. The results suggest the potential use of PPMMEu in bioprobes and gene vectors. 相似文献
We have developed a stable and sensitive nonenzymatic glucose sensor by modifying a glassy carbon electrode (GCE) with a composite incorporating nickel(II) oxides and reduced graphene. The oxides were generated by directly electrodepositing nickel on the GCE with a graphene modifier using a multi-potential pulse process, and then oxidizing nickel to nickel(II) oxides by potential cycling. In comparison to the conventional nickel(II) oxides-modified GCE, this new nickel(II) oxides-graphene modified GCE (NiO-GR/GCE) has an about 1.5 times larger current response toward the nonenzymatic oxidation of glucose in alkaline media. The response to glucose is linear in the 20 μM to 4.5 mM concentration range. The limit of detection is 5 μM (at a S/N of 3), and the response time is very short (<3 s). Other beneficial features include selectivity, reproducibility and stability. A comparison was performed on the determination of glucose in commercial red wines by high-performance liquid chromatography (HPLC) and revealed the promising aspects of this sensor with respect to the determination of glucose in real samples.
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A stable and sensitive nonenzymatic glucose sensor is developed by preparing the nickel(II) oxides-reduced graphene nanocomposite modified glassy carbon electrode (NiO-GR/GCE), and then used to detect the glucose contents in the commercial red wines. This NiO-GR/GCE also has a high selectivity 相似文献
The interactions between bovine serum albumin (BSA) and polymer (poly (METAC-co-NIPAm-co-Eu(AA)3Phen), PMNEu) containing rare earth element (Europium) were detailedly investigated by both of experimental techniques, such as fluorescence spectroscopic analysis, zeta-potential characterization, hydrodynamic size measurements and transmission electron microscopy (TEM) observation, and theoretical calculations. As a result, we concluded that PMNEu could interact with BSA through electrostatic force and quench the fluorescence of BSA, which was regarded as the static quenching mechanism. In addition, the binding constant and binding sites number of BSA with PMNEu were calculated, and the distance between PMNEu and BSA was also estimated to be 1.9?nm based on Föster’s theory. Furthermore, the two fluorescence peaks of PMNEu at 594?nm and 618?nm were detected, and the density of them increased with the more BSA being added to couple with PMNEu. Additionally, The zeta-potential results confirmed the electrostatic interaction mode between BSA and PMNEu, which was concluded with the previous thermodynamic analysis. At last, the results from the hydrodynamic size measurement had a good agreement with those from the TEM observation about the structure and size variation during the complexation of PMNEu with different concentrations of BSA. 相似文献