Inexact restoration method for derivative-free optimization with smooth constraints

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)A new method is introduced for solving constrained optimization problems in which the derivatives of the constraints are available but the derivatives of the objective function are not. The method is based on the inexact restoration framework, by means of which each iteration is divided in two phases. In the first phase one considers only the constraints, in order to improve feasibility. In the second phase one minimizes a suitable objective function subject to a linear approximation of the constraints. The second phase must be solved using derivative-free methods. An algorithm introduced recently by Kolda, Lewis, and Torczon for linearly constrained derivative-free optimization is employed for this purpose. Under usual assumptions, convergence to stationary points is proved. A computer implementation is described and numerical experiments are presented.A new method is introduced for solving constrained optimization problems in which the derivatives of the constraints are available but the derivatives of the objective function are not. The method is based on the inexact restoration framework, by means of23211891213CNPQ - CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICOFAPERJ - FUNDAÇÃO CARLOS CHAGAS FILHO DE AMPARO À PESQUISA DO ESTADO DO RIO DE JANEIROFAPESP - FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULOConselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)CNPq [E-26/171.164/2003-APQ1]FAPESP [FAPESP 2011-51305-0]FAPESP [03/09169-6, 06/53768-0, 07/06663-0, 08/00468-4]E-26/171.164/2003–APQ12011-51305-0; 03/09169-6; 06/53768-0; 07/06663-0; 08/00468-4sem informaçãoWe are indebted to associate editor Prof. Margaret Wright and two anonymous referees for many useful comments and remarks that led to significant improvement of this pape

Quasi-Newton approaches to Interior Point Methods for quadratic problems

Interior Point Methods (IPM) rely on the Newton method for solving systems of nonlinear equations. Solving the linear systems which arise from this approach is the most computationally expensive task of an interior point iteration. If, due to problem's inner structure, there are special techniques for efficiently solving linear systems, IPMs enjoy fast convergence and are able to solve large scale optimization problems. It is tempting to try to replace the Newton method by quasi-Newton methods. Quasi-Newton approaches to IPMs either are built to approximate the Lagrangian function for nonlinear programming problems or provide an inexpensive preconditioner. In this work we study the impact of using quasi-Newton methods applied directly to the nonlinear system of equations for general quadratic programming problems. The cost of each iteration can be compared to the cost of computing correctors in a usual interior point iteration. Numerical experiments show that the new approach is able to reduce the overall number of matrix factorizations and is suitable for a matrix-free implementation

Fixação de fósforo por um Latossolo e determinação do valor X.

Ensaio conduzido em laboratório para avaliar a capacidade de fixação de fósforo dos horizontes A1, A3 e B22 de latossolo roxo distrófico. Foi também determinado o valor X de WAUGH & FITS (1966) dos três horizontes. Os principais resultados são apresentados a seguir: O horizonte B22 foi que apresentou maior capacidade de fixação de fósforo, seguido pelo A3 e, finalmente, pelo A1. Os valores X encontrados foram 350 ppm225ppm e 175 ppm para os horizontes B22, A3 eA1, respectivamente. Houve uma relação muito estreita entre as quantidades de P adicionadas e as fixadas pelos três horizontes

Fixação de fósforo por um latossolo do Estado de Minas Gerais.

Foi estudada absorção do fósforo por amostras de três horizontes, A1, (0-22cm), A3(22-56cm) e B22(155-200cm), de um Latossolo do Estado de Minas Gerais por meio da isoterma de Langmuir. Os valores de adsorção máxima (b) e da constante de seletividade (K) calculados a partir da forma linear da equação de Langmuir foram correlacionados com algumas características físicas e químicas apresentadas pelos citados horizontes. Os resultados encontrados permitiram concluir que: As isotérmicas de adsorção mostram duas regiões distintas: aquela em que o fosfato é fortemente retido foi convenientemente descrita pela equação de Langmuir. Em virtude da diversidade das características físicas e químicas dos horizontes houve grande variação nos valores de adsorção máxima (b) e da constante seletividade (K)

Interaction between lactose and cadmium chloride in aqueous solutions as seen by diffusion coefficients measurements

Diffusion coefficients of an aqueous system containing cadmium chloride 0.100 mol · dm−3 and lactose at different concentrations at 25 °C have been measured, using a conductimetric cell and an automatic apparatus to follow diffusion. The cell relies on an open-ended capillary method and a conductimetric technique is used to follow the diffusion process by measuring the resistance of a solution inside the capillaries, at recorded times. From these results and by ab initio calculations, it was possible to obtain a better understanding of the effect of lactose on transport of cadmium chloride in aqueous solutions

1,5-Bis(2,5-dimethyl-1H-pyrrol-1-yl)naphthalene

In the title compound, C22H22N2, the asymmetric unit contains one half-mol­ecule. A crystallographic inversion centre is located at the mid-point of the bond common to both rings, in the central naphthalene unit. Quantum-mechanical ab initio calculations on the isolated mol­ecule showed that the minimum energy configuration occurs when the naphthalene ring system and the pyrrolyl groups deviate only slightly from perpendicularity. In the crystal, due to the effects of crystal packing, the mol­ecule deviates by approximately 4° from the a priori expected ideal value of 90° [C—C—N—C torsion angle = 86.11 (15)°]

Diaqua­(6-bromo­picolinato-κ2 N,O)(nitrato-κ2 O,O)copper(II)

In the monomeric title complex, [Cu(C6H3BrNO2)(NO3)(H2O)2], the CuII ion is coordinated by a bidentate 6-bromo­picolinate ion, one nitrate ion and two water mol­ecules in a geometry inter­mediate between five- and six-coordinate. Conventional O—H⋯O hydrogen bonds link the complex mol­ecules, forming layers parallel to the ab plane