Generalized sensitivity analysis of nonlinear programs using a sequence of quadratic programs

ABSTRACT

Local sensitivity information is obtained for KKT points of parametric NLPs that may exhibit active set changes under parametric perturbations; under appropriate regularity conditions, computationally relevant generalized derivatives of primal and dual variable solutions of parametric NLPs are calculated. Ralph and Dempe obtained directional derivatives of solutions of parametric NLPs exhibiting active set changes from the unique solution of an auxiliary quadratic program. This article uses lexicographic directional derivatives, a newly developed tool in nonsmooth analysis, to generalize the classical NLP sensitivity analysis theory of Ralph and Dempe. By viewing said auxiliary quadratic program as a parametric NLP, the results of Ralph and Dempe are applied to furnish a sequence of coupled QPs, whose unique solutions yield generalized derivative information for the NLP. A practically implementable algorithm is provided. The theory developed here is motivated by widespread applications of nonlinear programming sensitivity analysis, such as in dynamic control and optimization problems.     

Contingent derivatives and regularization for noncoercive inverse problems

Abstract

We study the inverse problem of parameter identification in noncoercive variational problems that commonly appear in applied models. We examine the differentiability of the set-valued parameter-to-solution map using the first-order and the second-order contingent derivatives. We explore the inverse problem using the output least-squares and the modified output least-squares objectives. By regularizing the noncoercive variational problem, we obtain a single-valued regularized parameter-to-solution map and investigate its smoothness and boundedness. We also consider optimization problems using the output least-squares and the modified output least-squares objectives for the regularized variational problem. We give a complete convergence analysis showing that for the output least-squares and the modified output least-squares, the regularized minimization problems approximate the original optimization problems suitably. We also provide the first-order and the second-order adjoint method for the computation of the first-order and the second-order derivatives of the output least-squares objective. We provide discrete formulas for the gradient and the Hessian calculation and present numerical results.     

KINETIC STUDY OF ALKOXIDE PROMOTED DECOMPOSITION OF ORGANIC PHOSPHONIUM COMPOUNDS Evidence for Hexacovalent Intermediate

Abstract

This study reports rate data of the alkoxide promoted decomposition of triphenyl 3-hydroxypropyl phosphonium chloride, diphenyl di(3-hydroxypropyl)phosphonium chloride, and tetraphenyl phosphonium bromide. Comparison of kinetics, rate constants, and activation parameters of the alkoxide promoted decompositions points to different mechanism as compared to the hydroxyl promoted reaction. The alkoxide reaction is believed to proceed via a hexacovalent intermediate. Reasons for the hexacovalent route are discussed.     

ON THE PHOSPHORUS-31 CHEMICAL SHIFTS OF SUBSTITUTED TRIARYLPHOSPHINES

Abstract

The ³¹P chemical shifts of eleven (4-ZC₆H₄)₃P compounds show a slight correlation with the Hammet [sgrave]para constant of Z. The unusually large upfield chemical shifts of (2-ZC₆H₄)₃P compounds are attributed to an extreme “gamma” effect caused by the restricted conformations due to the steric influence of the ortho substituents. Chemical shifts are given for about thirty triarylphosphines, and group contributions to phosphine chemical shifts are listed for twenty-one aryl groups.     

Synthesis of some novel 5-substituted benzamido-6-arylamino-pyrazolo[3,4-D]pyrimidin-4-one derivatives for herbicidal activity

Abstract

Sixteen novel 3-methylthio-5-substituted benzamido-6-arylamino-1-phenyl-1H-pyrazolo[3,4-d]pyrimidin-4 (5H)-one derivatives (4a–p) were successfully synthesized from iminophosphoranes, aryl isocyanate, and substituted benzoylhydrazine. The structures of the title compounds were elucidated by FT-IR, ¹H NMR, ¹³C NMR, and HRMS. Herbicidal activity of the compounds 4a–p against Brassica napus (rape), Echinochloa crusgalli (barnyard grass), Cucumis sativus (cucumber), and Triticum aestivum (wheat) were determined. The results showed that 5-(2-chlorobenzamido)-6-phenylamino-3-methylthio-1-phenyl-1H-pyrazolo[3,4-d]pyrimidin-4 (5H)-one (4c) displayed remarkable inhibition activity against the stalk and root of rape with 100% inhibition rate at the dosages of 10?mg/L and 100?mg/L, and 5-(4-nitrobenzamido)-6-phenylamino-3-methylthio-1-phenyl-1H-pyrazolo[3,4-d]pyrimidin-4 (5H) -one (4d) exhibited excellent activity against the stalk and root of barnyard grass with 100% inhibition rate at the same dosages.     

Silica Sulfuric Acid: An Efficient,Reusable, Heterogeneous Catalyst for the One-Pot,Five-Component Synthesis of Highly Functionalized Piperidine Derivatives

A series of highly functionalized piperidine derivatives was synthesized through one-pot, five-component reaction of aldehydes, amines, and β-ketoesters. Silica sulfuric acid efficiently catalyzes the reaction to afford the corresponding piperidine derivatives in good yields. As a representative example, heating of 4-methylaninle, 4-fluorobezaldehyde, and methyl-acetoacetate in methanol in the presence of silica sulfuric acid furnished the corresponding ethyl 2,6-bis(4-fluorophenyl)-1-p-tolyl-4-(p-tolylamino)-1,2,5,6-tetrahydropyridine-3-carboxylate in excellent yield (85%). Most of the synthesized compounds were screened in vitro for their antibacterial and antifungal activities. Most of compounds showed significant antibacterial activity.     

DFT study of the physicochemical characteristics and spectral behavior of new 8‐substituted 1,3,7‐trimethylxanthines

Nine biologically active theophylline derivatives were investigated using quantum chemical methods (density functional theory level). All calculations were performed at B3LYP/6‐31G** level of theory. The electrostatic potential charges, highest occupied molecular orbital (HOMO)/lowest unoccupied molecular orbital (LUMO) gap, dipole moment, vibration frequencies, and electronic spectra were calculated. Log P was determined by Ghose‐Crippen method. All of the compounds under study are polar and negatively charged, which is necessary for their interaction with the receptors/enzymes. Majority of the compounds are lipophilic and they can easily diffuse through the cell membrane. The observed differences between the calculated and the experimental vibration frequencies in the Fourier Transform Infrared Spectroscopy (FTIR) spectra are established to be mainly in NH and OH bands, due to hydrogen bonds formation. The discrepancies between theoretical and experimental electronic spectra may be due to vibration effects and H‐bonding with the solvent molecules. The obtained results show that this type of spectrum is formed mainly by the xanthine fragment of the molecule, especially in the fingerprint region. All calculated properties could be useful for future qualitative‐structure activity relationship (QSAR) analysis. © 2012 Wiley Periodicals, Inc.     

Synthesis of Benzimidazoles via Iron-Catalyzed Aerobic Oxidation Reaction of Imine Derivatives with o-Phenylenediamine

A simple and efficient protocol for preparing benzimidazoles via Fe(NO₃)₃ · 9H₂O-catalyzed aerobic oxidation reaction of imine derivatives with o-phenylenediamine. This process uses air as an economical and green oxidant, tolerates a wide range of substrates, and affords the targeted benzimidazoles in moderate to excellent yields.     

Efficient Preparation of Hybrid Linear‐Branched Esters of PEG‐PEE Derivatives

A simple and efficient preparation of a number of hybrid linear‐branched PEG esters are described. The polymers are generated by direct coupling of PEG–carboxylic acids and a variety of pentaerythritol ethoxylates using carbon tetrabromide catalyst.     

Microwave‐Assisted Solid‐State Synthesis and Characterization of Thiohydantoin Derivatives

Abstract

A new and efficient solid‐state method for the preparation of thiohydantoins is reported. With this method, twelve thiohydantoin compounds have been synthesized in good to excellent yields (81–92%). In addition, this method has the advantages of high yields, a cleaner reaction, simple methodology, and short reaction times.