Derivative-free optimization and filter methods to solve nonlinear constrained problems

In real optimization problems, usually the analytical expression of the objective function is not known, nor its derivatives, or they are complex. In these cases it becomes essential to use optimization methods where the calculation of the derivatives, or the verification of their existence, is not necessary: the Direct Search Methods or Derivative-free Methods are one solution. When the problem has constraints, penalty functions are often used. Unfortunately the choice of the penalty parameters is, frequently, very difficult, because most strategies for choosing it are heuristics strategies. As an alternative to penalty function appeared the filter methods. A filter algorithm introduces a function that aggregates the constrained violations and constructs a biobjective problem. In this problem the step is accepted if it either reduces the objective function or the constrained violation. This implies that the filter methods are less parameter dependent than a penalty function. In this work, we present a new direct search method, based on simplex methods, for general constrained optimization that combines the features of the simplex method and filter methods. This method does not compute or approximate any derivatives, penalty constants or Lagrange multipliers. The basic idea of simplex filter algorithm is to construct an initial simplex and use the simplex to drive the search. We illustrate the behavior of our algorithm through some examples. The proposed methods were implemented in Java.

Derivative-free nonlinear optimization filter simplex

The filter method is a technique for solving nonlinear programming problems. The filter algorithm has two phases in each iteration. The first one reduces a measure of infeasibility, while in the second the objective function value is reduced. In real optimization problems, usually the objective function is not differentiable or its derivatives are unknown. In these cases it becomes essential to use optimization methods where the calculation of the derivatives or the verification of their existence is not necessary: direct search methods or derivative-free methods are examples of such techniques. In this work we present a new direct search method, based on simplex methods, for general constrained optimization that combines the features of simplex and filter methods. This method neither computes nor approximates derivatives, penalty constants or Lagrange multipliers.

Synthesis of new 1,8-dihydroxy-9h-xanthen-9-ones

XXVth European Colloquium on Heterocyclic Chemistry, Reading, UK, 13 – 17 Agosto de 2012.

Protein-ligand docking study: diterpenes from Juniperus brevifolia as anticancer and antimicrobial agentes

REDCAT: Natural Products and related Redox Catalysts: Basic Research and Applications in Medicine and Agriculture, Aveiro, 25-27 Novembro de 2012.

Bioactive meroditerpenes from Cystoseira abies-marina, collected from the coast of S. Miguel island

3rd Portuguese Meeting on Medicinal Chemistry and 1st Portuguese-Spanish-Brazilian Meeting on Medicinal Chemistry, Aveiro, 28-30 Novembro 2012.

Synthesis and antioxidant activity of new xanthone-type compounds

3rd Portuguese Meeting on Medicinal Chemistry and 1st Portuguese-Spanish-Brazilian Meeting on Medicinal Chemistry, Aveiro, 28-30 Novembro 2012.

New xanthenodione: synthesis and antioxidant activity evaluation

6th Spanish-Portuguese-Japanese Organic Chemistry Symposium, Lisboa, de 18 a 20 de Julho de 2012 (Poster Communication).

Organic compounds isolated from Juniperus brevifolia bark

10º Encontro Nacional de Química Orgânica e 1º Simpósio Luso-Brasileiro de Química Orgânica, Lisboa, 4-6 Setembro de 2013

New syntheses of potential biologically active xanthones and benzoxanthones

10º Encontro Nacional de Química Orgânica e 1º Simpósio Luso-Brasileiro de Química Orgânica, Lisboa, 4-6 Setembro de 2013.

Synthesis, structure and electrochemical behaviour of Na, Mg-II, Mn-II, Cd-II and Ni-II complexes of 3-(2-carboxyphenylhydrazone)pentane-2,4-dione

Mononuclear manganese(II) [Mn(kappa O-HL)(2)(CH3OH)(4)] (4), nickel(II) [Ni(kappa O-2, kappa N-L)(H2O)(3)] (5), cadmium(II) [Cd(kappa O-2-HL)(2)(CH3OH)(3)] (7), tetranuclear zinc(II) [Zn-4(mu-OH)(2)(1 kappa O:2 kappa O-HL)(4)(kappa O-HL)(2)(H2O)(4)] (6) and polynuclear aqua sodium(I) [Na(H2O)(2)(mu-H2O)(2)](n)(HL)(n) (2) and magnesium(II) [Mg(OH)(H2O)(mu-H2O)(2)](n)(-HL)(n) (3) complexes were synthesized using 3-(2-carboxyphenyl-hydrazone)pentane-2,4-dione (H2L, 1) as a ligand precursor. The complexes were characterized by single crystal X-ray diffraction, elemental analysis, IR, H-1 and C-13 NMR (for 2, 3, 6 and 7) spectroscopies. Mono- or dianionic deprotonated derivatives of H2L display different coordination modes and lead to topologies and nuclearities of the complexes depending on metal ions and conditions used for the syntheses. Extensive intermolecular H-bonds form supramolecular arrangements in 1D chains (4 and 6), 1D chains of the organic anion and 2D networks of the metal-aqua aggregates (2 and 3), 2D networks (7) or even 3D frameworks (5). Electrochemical studies, by cyclic voltammetry and controlled potential electrolysis, show ligand centred redox processes as corroborated by theoretical DFT calculations in terms of LUMO and HOMO compositions. (C) 2012 Elsevier Ltd. All rights reserved.

Production of hydroxamic acids by immobilized Pseudomonas aeruginosa cells Kinetic analysis in reverse micelles

Intact cells from Pseudomonas aeruginosa strain L10 containing amidase were used as biocatalysts both free and immobilized in a reverse micellar system. The apparent kinetic constants for the transamidation reaction in hydroxamic acids synthesis, were determined using substrates such as aliphatic, amino acid and aromatic amides and esters, in both media. In reverse micelles, K-m values decreased 2-7 fold relatively to the free biocatalyst using as substrates acetamide, acrylamide, propionamide and glycinamide ethyl ester. We have concluded that overall the affinity of the biocatalyst to each substrate increases when reactions are performed in the reversed micellar system as opposed to the buffer system. The immobilized biocatalyst in general, exhibits higher stability and faster rates of reactions at lower substrates concentration relatively to the free form, which is advantageous. Additionally, the immobilization revealed to be suitable for obtaining the highest yields of hydroxamic acids derivatives, in some cases higher than 80%. (C) 2013 Elsevier B.V. All rights reserved.

Synthesis of new Fe(II) and Ru(II) eta(5)-monocyclopentadienyl compounds showing significant second order NLO properties

A series of new ruthenium(II) complexes of the general formula [Ru(eta(5)-C5H5)(PP)(L)][PF6] (PP = DPPE or 2PPh(3), L = 4-butoxybenzonitrile or N-(3-cyanophenyl)formamide) and the binuclear iron(II) complex [Fe(eta(5)-C5H5)(PP)(mu-L)(PP)(eta(5)-C5H5)Fe][PF6](2) (L = (E)-2-(3-(4-nitrophenyl)allylidene)malononitrile, that has been also newly synthesized) have been prepared and studied to evaluate their potential in the second harmonic generation property. All the new compounds were fully characterized by NMR, IR and UV-Vis spectroscopies and their electrochemistry behaviour was studied by cyclic voltammetry. Quadratic hyperpolarizabilities (beta) of three of the complexes have been determined by hyper-Rayleigh scattering (HRS) measurements at fundamental wavelength of 1500 nm and the calculated static beta(0) values are found to fall in the range 65-212 x 10(-30) esu. Compound presenting beta(0) = 212 x 10(-30) esu has revealed to be 1.2 times more efficient than urea standard in the second harmonic generation (SHG) property, measured in the solid state by Kurtz powder technique, using a Nd:YAG laser (1064 nm). (C) 2013 Elsevier B.V. All rights reserved.

Synthesis, characterization, electrochemical behavior and in vitro protein tyrosine kinase inhibitory activity of the cymene-halogenobenzohydroxamato [Ru(eta(6)-cymene)(bha)Cl] complexes

The ruthenium(II)-cymene complexes [Ru(eta(6)-cymene)(bha)Cl] with substituted halogenobenzohydroxamato (bha) ligands (substituents = 4-F, 4-Cl, 4-Br, 2,4-F-2, 3,4-F-2, 2,5-F-2, 2,6-F-2) have been synthesized and characterized by elemental analysis, IR, H-1 NMR, C-13 NMR, cyclic voltammetry and controlled-potential electrolysis, and density functional theory (DFT) studies. The compositions of their frontier molecular orbitals (MOs) were established by DFT calculations, and the oxidation and reduction potentials are shown to follow the orders of the estimated vertical ionization potential and electron affinity, respectively. The electrochemical E-L Lever parameter is estimated for the first time for the various bha ligands, which can thus be ordered according to their electron-donor character. All complexes exhibit very strong protein tyrosine kinase (PTK) inhibitory activity, even much higher than that of genistein, the clinically used PTK inhibitory drug. The complex containing the 2,4-difluorobenzohydroxamato ligand is the most active one, and the dependences of the PTK activity of the complexes and of their redox potentials on the ring substituents are discussed. (C) 2012 Elsevier B.V. All rights reserved.

Futuros financeiros: uma abordagem aos commodities de algodão

Dissertação de Mestrado Apresentado ao Instituto de Contabilidade e Administração do Porto para a obtenção do grau de Mestre em Contabilidade e Finanças, sob orientação de Mestre José Carlos Pedro

Pittosporum Undulatum and Hedychium Gardnerianum: nutritive value and secondary metabolites on cattle reproductive performances

Hedychium gardnerianum (HG) and Pittospporum undulatum (PU) are invasive plants all over the world, being in the Azores supplied to cattle on periods of shortage food. As these plants produce secondary metabolites, including a diverse range of phytochemicals compounds, the aim of the presente study is to identify how these metabolites can be related to animal’s reproductive performances. For such purpose, plants were harvested on winter, compounds extracted by method of decoction and analysed by combination of liquid chromatography and mass spectrometry as well as highperformance liquid chromatography. For nutritive evaluations, Van Soest and Weende methodologies were used. In HG quercetin-3, 4'-di-O-betaglucopyranoside, myricetin rhamnoside, quercetin rhamnoside, and gibberellin A1 and A8 were identified, while for PU were found cafeic acid derivatives, including dicaffeoylquinic acid and caffeoylquinic acid. In nutritional terms, these plants can be considered as poor, presenting percentages of dry matter (DM%) of 16.34% and 40.39%, respectively for HG and PU. Values for ash 10.4%, crude protein (CP) 7.75%, neutral detergent fiber (NDF) 64.5, acid detergent fiber (ADF) 34.69%, acid detergent lignin (ADL) 3.47% and ether extract (EE) 2.03% were found for HG. For PU values were ash 6.64%, CP 6.11%, NDF 43.84%, acid ADF 35.57%, ADL 3.56% and EE 2.71%. This study clearly indicated that, besides their low nutritive values, these plants can be used to feed ruminants, especially when pasture lacks. Nevertheless, as some compounds, namely the caffeoylquinic and dicaffeoylquinic acids, are known to be associated to physiological reproductive mechanisms, one could speculate that these compounds can be directly or indirectly associated to reproductive performances in bovine fed with these plants.