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.”     

Schauder Bases under Uniform Renormings

Let X be a separable superreflexive Banach space with a Schauder basis. We prove the existence of an equivalent uniformly smooth (resp. uniformly rotund) renorming under which the given basis is monotone. First author supported by the grants MTM2005-08379 of MECD (Spain), 00690/PI/04 of Fundación Séneca (CARM, Spain) and AP2003-4453 of MECD (Spain), Second author supported by AV0Z10190503 and A100190502.     

Resonance and non-resonance in a problem of boundedness

This paper studies the existence of bounded solutions of a forced non-linear differential equation of arbitrary order. Necessary and sufficient conditions for the existence of such solutions are obtained. These results are inspired by classical results on the periodic problem, both in the resonant and non-resonant cases.

     

Geodesics on lorentzian manifolds with quasi-convex boundary

In this paper we study existence and multiplicity results of geodesics joining two given events in Lorentzian manifolds with lack of geodesic completeness. The considered Lorentzian manifolds are not necessarily static or stationary and satisfy a condition of convexity on the boundary. work supported by M.U.R.S.T. research founds 40%–60% 1992     

Synthesis and Crystal Structures of Neutral Complexes of Tellurium(IV) – [PhTeX3L](X = Br,I; L = ethylenethiourea)

A three‐step one‐pot synthetic procedure to synthesize the neutral tellurium(IV) coordination compounds PhTeX₃L (X = Br, I and L = ethylenethiourea) has been developed and is described in this article. Oxidative halogenation of PhTeTePh in methanol generates the tellurium(II) derivative, PhTeX, which is subsequently complexed with ethylenethiourea, and, finally, further oxidative addition of additional halogen affords the corresponding tellurium(IV) compound PhTeX₃L in good yields. The final product was obtained by the slow evaporation of the reaction mixture as black crystals. The X‐ray structural analyses of the compounds show Te···X and X···X secondary interactions in the solid state and suggest a weak dependence of the formation of supramolecular assemblies on the nature of the halogen bonded to the tellurium atom.     

Equilibrium real gas computations using Marquina's scheme

Marquina's approximate Riemann solver for the compressible Euler equations for gas dynamics is generalized to an arbitrary equilibrium equation of state. Applications of this solver to some test problems in one and two space dimensions show the desired accuracy and robustness. Copyright © 2003 John Wiley & Sons, Ltd.     

Exact boundary controllability in problems of transmission for the system of electromagneto‐elasticity

This paper considers transmission problem for the system of electromagneto‐elasticity having piecewise constant coefficients in a bounded domain. The result on exact boundary controllability is obtained provided the interfaces, where the coefficients have a jump discontinuity, are all star‐shaped with respect to one and the same point and the coefficients satisfy a certain monotonicity conditions. Copyright © 2001 John Wiley & Sons, Ltd.     

Olefin epoxidations in the ionic liquid [C4mim][PF6] catalysed by oxodiperoxomolybdenum species in situ generated from molybdenum trioxide and urea–hydrogen peroxide: The synthesis and molecular structure of [Mo(O)(O2)2(4-MepyO)2]·H2O

Commercially available molybdenum(VI) compounds, including molybdenum trioxide, were successfully employed as catalyst precursors in the epoxidation of olefins with urea–hydrogen peroxide adduct (UHP) in the ionic liquid 1-butyl-3-methylimidazolium hexafluorophosphate, [C₄mim][PF₆]. After oxidation, the corresponding epoxides were isolated by extraction with diethyl ether. Additionally the ionic liquid–catalyst mixture was recycled and reused in further catalytic cycles. The catalytic species is assumed to be an oxodiperoxomolybdenum species which forms in situ. A representative complex of this type was thus isolated and characterised. Reaction of excess 4-methylpyridine-1-oxide (4-MepyO) with MoO₃ dissolved in aqueous hydrogen peroxide afforded [Mo(O)(O₂)₂(4-MepyO)₂]·H₂O (1) as yellow crystals. Compound 1, an active epoxidation catalyst, was subsequently characterised and its structure determined by X-ray crystallography.     

Toughness enhancement of cellulose nanocomposites by alkali treatment of the reinforcing cellulose nanofibers

Nanocomposites were produced with NaOH aqueous solution-treated microfibrillated cellulose (MFC) and phenolic resin, and the mechanical properties were compared with their microcomposite counterparts based on pulp fiber. Tensile tests showed that strong alkali-treated MFC nanocomposites with resin content around 20 wt.% achieved strain at fracture values two times higher than those of untreated MFC nanocomposites and five times higher than those of untreated pulp microcomposites. The improvement in work of fracture of alkali-treated MFC nanocomposites was attributed to the ductility of the nanofibers caused by transformations in the amorphous regions along the cellulose microfibrils.