Adaptive smoothing algorithms for nonsmooth composite convex minimization

We propose an adaptive smoothing algorithm based on Nesterov’s smoothing technique in Nesterov (Math Prog 103(1):127–152, 2005) for solving “fully” nonsmooth composite convex optimization problems. Our method combines both Nesterov’s accelerated proximal gradient scheme and a new homotopy strategy for smoothness parameter. By an appropriate choice of smoothing functions, we develop a new algorithm that has the \(\mathcal {O}\left( \frac{1}{\varepsilon }\right) \)-worst-case iteration-complexity while preserves the same complexity-per-iteration as in Nesterov’s method and allows one to automatically update the smoothness parameter at each iteration. Then, we customize our algorithm to solve four special cases that cover various applications. We also specify our algorithm to solve constrained convex optimization problems and show its convergence guarantee on a primal sequence of iterates. We demonstrate our algorithm through three numerical examples and compare it with other related algorithms.     

New flavan and benzil isolated from Fissistigma latifolium

Further investigation of the methanolic extract of Fissistigma latifolium resulted in two new compounds whose structures were assigned as 2,5,6,7-tetramethoxyflavan (1) and 2'-hydroxy-4',5',6'-trimethoxybenzil (2). These two compounds were determined on the basis of chemical and spectroscopic evidences. Compound 2 is the first report of benzil from Fissistigma species. 2,5,6,7-Tetramethoxyflavan (1) showed a potent inhibitory effect on superoxide anion production in formyl-L-methionyl-L-leucyl-L-phenylalanine (fMLP)/cytochalasin B (CB)-activated human neutrophils.     

DNA fragment conformations. I—methods for the assignment of DNA fragment proton resonances. 1H NMR spectra of dApTpGpT and dApCpApTpGpT

A general method for the assignment of DNA fragment proton resonances, especially for the sugar protons, has been presented and used to interpret the 400 MHz proton spectra of dApTpGpT and dApCpApTpGpT in neutral aqueous solution. Only fine splittings of about 3 Hz are observed in the H-2″ resonances, and the total splitting is larger for the H-2′ (≈29 Hz) than for the H-2″ (22–23 Hz) multiplets. The purine and pyrimidine resonances can be distinguished on the basis of the H-2″ and H-2″ chemical shifts. The resonances of the H-2′ and H-2″ protons (above and below the sugar plane, respectively) of dA and dG exhibit chemical shifts of 2.65—2.80 ppm, while those of dC and dT residues are located at higher fields between 1.95 and 2.40 ppm. At high temperature (≥60°C), δH-2′>YδH-2″ for the purine family, while δH-2′ « δH-2″ in the case of the pyrimidine family. Except for the terminal residue, the H-3′ resonances of dA and dG are located at lower fields compared with those of the dC and dT residues. The same is true for the H-4′ resonances. In general δA_1′>δG_1′ and in the case of self complementary duplexes the H-1′ and H-2′ chemical shift variations versus temperature are found to be larger for the dC than for the dT residues.     

A hybrid stochastic optimization framework for composite nonconvex optimization

Mathematical Programming - We introduce a new approach to develop stochastic optimization algorithms for a class of stochastic composite and possibly nonconvex optimization problems. The main idea...     

Adaptive inexact fast augmented Lagrangian methods for constrained convex optimization

In this paper we study two inexact fast augmented Lagrangian algorithms for solving linearly constrained convex optimization problems. Our methods rely on a combination of the excessive-gap-like smoothing technique introduced in Nesterov (SIAM J Optim 16(1):235–249, 2005) and the general inexact oracle framework studied in Devolder (Math Program 146:37–75, 2014). We develop and analyze two augmented based algorithmic instances with constant and adaptive smoothness parameters, and derive a total computational complexity estimate in terms of projections on a simple primal feasible set for each algorithm. For the constant parameter algorithm we obtain the overall computational complexity of order \(\mathcal {O}(\frac{1}{\epsilon ^{5/4}})\), while for the adaptive one we obtain \(\mathcal {O}(\frac{1}{\epsilon })\) total number of projections onto the primal feasible set in order to achieve an \(\epsilon \)-optimal solution for the original problem.     

Modele de jonction B-Z danz un oligonucleotide synthetique comportant un site apurinique

The synthesis of the tridecadeoxynucleotide d(C-G-m⁵C-G-C-G-X-A-C-A-T-G-T), were X is a no-base residue, is described. The NMR, IR and CD studies at various salt concentrations and temperatures of the modified oligomer, show that the B and Z conformations are simultaneously present in the same duplex.