Interior-Point Solver for Large-Scale Quadratic Programming Problems with Bound Constraints

In this paper, we present an interior-point algorithm for large and sparse convex quadratic programming problems with bound constraints. The algorithm is based on the potential reduction method and the use of iterative techniques to solve the linear system arising at each iteration. The global convergence properties of the potential reduction method are reassessed in order to take into account the inexact solution of the inner system. We describe the iterative solver, based on the conjugate gradient method with a limited-memory incomplete Cholesky factorization as preconditioner. Furthermore, we discuss some adaptive strategies for the fill-in and accuracy requirements that we use in solving the linear systems in order to avoid unnecessary inner iterations when the iterates are far from the solution. Finally, we present the results of numerical experiments carried out to verify the effectiveness of the proposed strategies. We consider randomly generated sparse problems without a special structure. Also, we compare the proposed algorithm with the MOSEK solver. Research partially supported by the MIUR FIRB Project RBNE01WBBB “Large-Scale Nonlinear Optimization.”     

Spectrophotometric determination of fusicoccin

Fusicoccin incubated for 17 h in 6 M HCl at 37°C gives rise to a chromophoric system having an absorption maximum at 555 nm. A colorimetric method for the determination of pure fusicoccin and of fusicoccin in fermentation liquors and infected plant tissues is described. The method is useful for 50–800 μg of fusicoccin.     

New synthesis of condensed hydropyridazine derivatives V

The reactivity of pyrrole derivatives towards the semicarbazone of ω-bromoacetophenone has been reported. Substituents at position 1 of the pyrrole ring greatly affect the course of the reaction. 1,4,4a,4b,5,8,8a,8b-Octahydro-9H-pyrrolo[2,3-c:4,5-c′]dipyridazine derivative or α- and α,α-pyrrolyl derivatives were obtained depending on the substituents. The structures reported were assigned on the basis of satisfactory analytical and spectroscopic data.     

Tereoselective total synthesis of racemic grandisol : An improved convenient procedure

(±) Grandisol has been stereoselectively synthesized in a 31% overall yield by a practical and convenient procedure employing the Salomon photobicyclization as the key-step.     

Stereospecific synthesis of γ-butyrolactones from acyclic vinyl sulfoxides: an asymmetric synthesis of optically pure oak lactones

The sulfoxide-directed lactonization of several trisubstituted vinyl sulfoxides with dichloroketene proceeds in a completely stereospecific manner. The lactonization of (E) -3 (R) -$\text{p}$-tolylsulfinyloctene occurs with complete enantiospecificity to produce a precursor for the synthesis of optically pure oak lactones.     

Laser photochemistry: The intramolecular cyclization of carvone to carvonecamphor

Kr-ion laser irradiation of carvone ($\text{1}$) at 350.7 and 356.4 nm gave carvonecamphor ($\text{2}$) in a much higher yield (88%) than in conventional photochemistry, while ($\text{3}$) was a primary photo-by-product.