On the local convergence of a derivative-free algorithm for least-squares minimization

In Zhang et al. (accepted by SIAM J. Optim., 2010), we developed a class of derivative-free algorithms, called DFLS, for least-squares minimization. Global convergence of the algorithm as well as its excellent numerical performance within a limited computational budget was established and discussed in the same paper. Here we would like to establish the local quadratic convergence of the algorithm for zero residual problems. Asymptotic convergence performance of the algorithm for both zero and nonzero problems is tested. Our numerical experiments indicate that the algorithm is also very promising for achieving high accuracy solutions compared with software packages that do not exploit the special structure of the least-squares problem or that use finite differences to approximate the gradients.     

Coevolution of protein and RNA structures within a highly conserved ribosomal domain

The X-ray crystal structure of a ribosomal L11-rRNA complex with chloroplast-like mutations in both protein and rRNA is presented. The global structure is almost identical to that of the wild-type (bacterial) complex, with only a small movement of the protein alpha helix away from the surface of the RNA required to accommodate the altered protein residue. In contrast, the specific hydrogen bonding pattern of the mutated residues is substantially different, and now includes a direct interaction between the protein side chain and an RNA base edge and a water-mediated contact. Comparison of the two structures allows the observations of sequence variation and relative affinities of wild-type and mutant complexes to be clearly rationalized, but reinforces the concept that there is no single simple code for protein-RNA recognition.     

On high-frequency fatigue and dynamic properties at elevated temperature

The effects of elevated temperature and high strain rate on fatigue life and tensile properties were measured for annealed 316 stainless steel and titanium alloy 6Al?2Mo?4Zr?2Sn in the solution-heat-treated and aged condition. A 14-KHz magnetostriction oscillator was used for fatigue testing. This equipment was developed for operation in excess of 2000° F. A split Hopkinson pressure bar provided dynamic tensile data up to 1300° F at strain rates on the order of 10³ in./in./sec. An attempt was made to correlate the high-frequency-fatigue data with the dynamic tensile measurements by using the Manson fatiguelife-prediction methods. This paper contains the experimental results and discusses the analysis of these experiments.     

Second-order conditions for an exact penalty function

In this paper we give first- and second-order conditions to characterize a local minimizer of an exact penalty function. The form of this characterization gives support to the claim that the exact penalty function and the nonlinear programming problem are closely related.In addition, we demonstrate that there exist arguments for the penalty function from which there are no descent directions even though these points are not minimizers.This research is partially supported by the Natural Science and Engineering Research Council Grant No. A8639 and the U.S. Department of Energy.     

Development and kilogram-scale synthesis of mGlu5 negative allosteric modulator VU0424238 (auglurant)

This communication details the kilogram-scale synthesis of N-(5-fluoropyridin-2-yl)-6-methyl-4-(pyrimidin-5-yloxy)picolinamide (VU0424238, auglurant), a novel mGlu₅ negative allosteric modulator (NAM) developed as an alternative treatment for depression. The process highlights a challenging pyridine N-oxidation sequence, an S_NAr reaction, and the elimination of all chromatography steps (required in the medicinal chemistry route) with replacement by highly efficient recrystallizations (save one silica plug). The improved process was utilized for the preparation of a 1.2 kg toxicology batch, as well as a 2.82 kg GMP batch to support the Phase I trial, in very high purity (99.8%).     

Convergence of quasi-Newton matrices generated by the symmetric rank one update

Quasi-Newton algorithms for unconstrained nonlinear minimization generate a sequence of matrices that can be considered as approximations of the objective function second derivatives. This paper gives conditions under which these approximations can be proved to converge globally to the true Hessian matrix, in the case where the Symmetric Rank One update formula is used. The rate of convergence is also examined and proven to be improving with the rate of convergence of the underlying iterates. The theory is confirmed by some numerical experiments that also show the convergence of the Hessian approximations to be substantially slower for other known quasi-Newton formulae.The work of this author was supported by the National Sciences and Engineering Research Council of Canada, and by the Information Technology Research Centre, which is funded by the Province of Ontario.     

Nonlinear programming via an exact penalty function: Asymptotic analysis

In this paper we consider the final stage of a ‘global’ method to solve the nonlinear programming problem. We prove 2-step superlinear convergence. In the process of analyzing this asymptotic behavior, we compare our method (theoretically) to the popular successive quadratic programming approach.