Augmented Lagrangian methods under the constant positive linear dependence constraint qualification

Two Augmented Lagrangian algorithms for solving KKT systems are introduced. The algorithms differ in the way in which penalty parameters are updated. Possibly infeasible accumulation points are characterized. It is proved that feasible limit points that satisfy the Constant Positive Linear Dependence constraint qualification are KKT solutions. Boundedness of the penalty parameters is proved under suitable assumptions. Numerical experiments are presented.

Uma investigação da influência do parâmetro de barreira na solução do problema de fluxo de potência ótimo

Pós-graduação em Engenharia Elétrica - FEB

Processamento interpretativo de dados magnetométricos e inversão de dados gravimétricos aplicados à prospecção de hidrocarbonetos

Apresentamos dois métodos de interpretação de dados de campos potenciais, aplicados à prospecção de hidrocarbonetos. O primeiro emprega dados aeromagnéticos para estimar o limite, no plano horizontal, entre a crosta continental e a crosta oceânica. Este método baseia-se na existência de feições geológicas magnéticas exclusivas da crosta continental, de modo que as estimativas das extremidades destas feições são usadas como estimativas dos limites da crosta continental. Para tanto, o sinal da anomalia aeromagnética na região da plataforma, do talude e da elevação continental é amplificado através do operador de continuação analítica para baixo usando duas implementações: o princípio da camada equivalente e a condição de fronteira de Dirichlet. A maior carga computacional no cálculo do campo continuado para baixo reside na resolução de um sistema de equações lineares de grande porte. Este esforço computacional é minimizado através do processamento por janelas e do emprego do método do gradiente conjugado na resolução do sistema de equações. Como a operação de continuação para baixo é instável, estabilizamos a solução através do funcional estabilizador de primeira ordem de Tikhonov. Testes em dados aeromagnéticos sintéticos contaminados com ruído pseudo-aleatório Gaussiano mostraram a eficiência de ambas as implementações para realçar os finais das feições magnéticas exclusivas da crosta continental, permitindo o delineamento do limite desta com a crosta oceânica. Aplicamos a metodologia em suas duas implementações a dados aeromagnéticos reais de duas regiões da costa brasileira: Foz do Amazonas e Bacia do Jequitinhonha. O segundo método delineia, simultaneamente, a topografia do embasamento de uma bacia sedimentar e a geometria de estruturas salinas contidas no pacote sedimentar. Os modelos interpretativos consistem de um conjunto de prismas bidimensionais verticais justapostos, para o pacote sedimentar e de prismas bidimensionais com seções verticais poligonais para as estruturas salinas. Estabilizamos a solução, incorporando características geométricas do relevo do embasamento e das estruturas salinas compatíveis com o ambiente geológico através dos estabilizadores da suavidade global, suavidade ponderada e da concentração de massa ao longo de direções preferenciais, além de vínculos de desigualdade nos parâmetros. Aplicamos o método a dados gravimétricos sintéticos produzidos por fontes 2D simulando bacias sedimentares intracratônicas e marginais apresentando densidade do pacote sedimentar variando com a profundidade segundo uma lei hiperbólica e abrigando domos e almofadas salinas. Os resultados mostraram que o método apresenta potencial para delinear, simultaneamente, as geometrias tanto de almofadas e domos salinos, como de relevos descontínuos do embasamento. Aplicamos o método, também, a dados reais ao longo de dois perfis gravimétricos sobre as Bacias de Campos e do Jequitinhonha e obtivemos interpretações compatíveis com a geologia da área.

Uso das rotações de givens modificadas como um método direto para obtenção e atualização das soluções em sistemas com acumulação seqüencial de dados

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Matrix-vector multiplication and triangular linear solver using GPGPU for symmetric positive definite matrices derived from elliptic equations

The modern GPUs are well suited for intensive computational tasks and massive parallel computation. Sparse matrix multiplication and linear triangular solver are the most important and heavily used kernels in scientific computation, and several challenges in developing a high performance kernel with the two modules is investigated. The main interest it to solve linear systems derived from the elliptic equations with triangular elements. The resulting linear system has a symmetric positive definite matrix. The sparse matrix is stored in the compressed sparse row (CSR) format. It is proposed a CUDA algorithm to execute the matrix vector multiplication using directly the CSR format. A dependence tree algorithm is used to determine which variables the linear triangular solver can determine in parallel. To increase the number of the parallel threads, a coloring graph algorithm is implemented to reorder the mesh numbering in a pre-processing phase. The proposed method is compared with parallel and serial available libraries. The results show that the proposed method improves the computation cost of the matrix vector multiplication. The pre-processing associated with the triangular solver needs to be executed just once in the proposed method. The conjugate gradient method was implemented and showed similar convergence rate for all the compared methods. The proposed method showed significant smaller execution time.

Direct in vitro and in vivo comparison of 161Tb and 177Lu using a tumour-targeting folate conjugate

Purpose The radiolanthanide 161Tb (T 1/2 = 6.90 days, Eβ− av = 154 keV) was recently proposed as a potential alternative to 177Lu (T 1/2 = 6.71 days, Eβ− av = 134 keV) due to similar physical decay characteristics but additional conversion and Auger electrons that may enhance the therapeutic efficacy. The goal of this study was to compare 161Tb and 177Lu in vitro and in vivo using a tumour-targeted DOTA-folate conjugate (cm09). Methods 161Tb-cm09 and 177Lu-cm09 were tested in vitro on folate receptor (FR)-positive KB and IGROV-1 cancer cells using a 3-(4,5-dimethylthiazol-2-yl)-2,5-diphenyltetrazolium bromide (MTT) viability assay. In vivo 161Tb-cm09 and 177Lu-cm09 (10 MBq, 0.5 nmol) were investigated in two different tumour mouse models with regard to the biodistribution, the possibility for single photon emission computed tomography (SPECT) imaging and the antitumour efficacy. Potentially undesired side effects were monitored over 6 months by determination of plasma parameters and examination of kidney function with quantitative SPECT using 99mTc-dimercaptosuccinic acid (DMSA). Results To obtain half-maximal inhibition of tumour cell viability a 4.5-fold (KB) and 1.7-fold (IGROV-1) lower radioactivity concentration was required for 161Tb-cm09 (IC50 ~0.014 MBq/ml and ~2.53 MBq/ml) compared to 177Lu-cm09 (IC50 ~0.063 MBq/ml and ~4.52 MBq/ml). SPECT imaging visualized tumours of mice with both radioconjugates. However, in therapy studies 161Tb-cm09 reduced tumour growth more efficiently than 177Lu-cm09. These findings were in line with the higher absorbed tumour dose for 161Tb-cm09 (3.3 Gy/MBq) compared to 177Lu-cm09 (2.4 Gy/MBq). None of the monitored parameters indicated signs of impaired kidney function over the whole time period of investigation after injection of the radiofolates. Conclusion Compared to 177Lu-cm09 we demonstrated equal imaging features for 161Tb-cm09 but an increased therapeutic efficacy for 161Tb-cm09 in both tumour cell lines in vitro and in vivo. Further preclinical studies using other tumour-targeting radioconjugates are clearly necessary to draw final conclusions about the future clinical perspectives of 161Tb.

Time trials on second-order and variable-learning-rate algorithms

The performance of seven minimization algorithms are compared on five neural network problems. These include a variable-step-size algorithm, conjugate gradient, and several methods with explicit analytic or numerical approximations to the Hessian.

Using interior point algorithms for the solution of linear programs with special structural features

Linear Programming (LP) is a powerful decision making tool extensively used in various economic and engineering activities. In the early stages the success of LP was mainly due to the efficiency of the simplex method. After the appearance of Karmarkar's paper, the focus of most research was shifted to the field of interior point methods. The present work is concerned with investigating and efficiently implementing the latest techniques in this field taking sparsity into account. The performance of these implementations on different classes of LP problems is reported here. The preconditional conjugate gradient method is one of the most powerful tools for the solution of the least square problem, present in every iteration of all interior point methods. The effect of using different preconditioners on a range of problems with various condition numbers is presented. Decomposition algorithms has been one of the main fields of research in linear programming over the last few years. After reviewing the latest decomposition techniques, three promising methods were chosen the implemented. Sparsity is again a consideration and suggestions have been included to allow improvements when solving problems with these methods. Finally, experimental results on randomly generated data are reported and compared with an interior point method. The efficient implementation of the decomposition methods considered in this study requires the solution of quadratic subproblems. A review of recent work on algorithms for convex quadratic was performed. The most promising algorithms are discussed and implemented taking sparsity into account. The related performance of these algorithms on randomly generated separable and non-separable problems is also reported.

Decision support system for contractor pre-qualification : artificial neural network model

The selection criteria for contractor pre-qualification are characterized by the co-existence of both quantitative and qualitative data. The qualitative data is non-linear, uncertain and imprecise. An ideal decision support system for contractor pre-qualification should have the ability of handling both quantitative and qualitative data, and of mapping the complicated nonlinear relationship of the selection criteria, such that rational and consistent decisions can be made. In this research paper, an artificial neural network model was developed to assist public clients identifying suitable contractors for tendering. The pre-qualification criteria (variables) were identified for the model. One hundred and twelve real pre-qualification cases were collected from civil engineering projects in Hong Kong, and eighty-eight hypothetical pre-qualification cases were also generated according to the “If-then” rules used by professionals in the pre-qualification process. The results of the analysis totally comply with current practice (public developers in Hong Kong). Each pre-qualification case consisted of input ratings for candidate contractors’ attributes and their corresponding pre-qualification decisions. The training of the neural network model was accomplished by using the developed program, in which a conjugate gradient descent algorithm was incorporated for improving the learning performance of the network. Cross-validation was applied to estimate the generalization errors based on the “re-sampling” of training pairs. The case studies show that the artificial neural network model is suitable for mapping the complicated nonlinear relationship between contractors’ attributes and their corresponding pre-qualification (disqualification) decisions. The artificial neural network model can be concluded as an ideal alternative for performing the contractor pre-qualification task.

Alleviating ‘overfitting’ via genetically-regularised neural network

A hybrid genetic algorithm/scaled conjugate gradient regularisation method is designed to alleviate ANN `over-fitting'. In application to day-ahead load forecasting, the proposed algorithm performs better than early-stopping and Bayesian regularisation, showing promising initial results.

Identification of a class of non-linear systems

This paper considers the on-line identification of a non-linear system in terms of a Hammerstein model, with a zero-memory non-linear gain followed by a linear system. The linear part is represented by a Laguerre expansion of its impulse response and the non-linear part by a polynomial. The identification procedure involves determination of the coefficients of the Laguerre expansion of correlation functions and an iterative adjustment of the parameters of the non-linear gain by gradient methods. The method is applicable to situations involving a wide class of input signals. Even in the presence of additive correlated noise, satisfactory performance is achieved with the variance of the error converging to a value close to the variance of the noise. Digital computer simulation establishes the practicability of the scheme in different situations.

Reliability Optimization using SLUMT

This paper is concerned with the reliability optimization of a spatially redundant system, subject to various constraints, by using nonlinear programming. The constrained optimization problem is converted into a sequence of unconstrained optimization problems by using a penalty function. The new problem is then solved by the conjugate gradient method. The advantages of this method are highlighted.

A modified least squares algorithm to treat associations in liquid alloys

The associated model for binary systems has been modified to include volume effects and excess entropy arising from preferential interactions between the associate and the free atoms or between the free atoms. Equations for thermodynamic mixing functions have been derived. An optimization procedure using a modified conjugate gradient method has been used to evaluate the enthalpy and entropy interaction energies, the free energy of dissociation of the complex, its temperature dependance and the size of the associate. An expression for the concentration—concentration structure factor [Scc (0)] has been deduced from the modified associated solution model. The analysis has been applied to the thermodynamic mixing functions of liquid Ga-Te alloys at 1120 K, believed to contain Ga2Te3 associates. It is observed that the modified associated solution model incorporating volume effects and terms for the temperature dependance of interaction energies, describes the thermodynamic properties of Ga-Te system satisfactorily.

Design options reduce exchanger cost

Heat exchanger design is a complex task involving the selection of a large number of interdependent design parameters. There are no established general techniques for optimizing the design, though a few earlier attempts provide computer software based on gradient methods, case study methods, etc. The authors felt that it would be useful to determine the nature of the optimal and near-optimal feasible designs to devise an optimization technique. Therefore, in this article they have obtained a large number of feasible designs of shell and tube heat exchangers, intended to perform a given heat duty, by an exhaustive search method. They have studied how their capital and operating costs varied. The study reveals several interesting aspects of the dependence of capital and total costs on various design parameters. The authors considered a typical shell and tube heat exchanger used in an oil refinery. Its heat duty, inlet temperature and other details are given.

Optimal control for the rolling pullout maneuver of a modern fighter aircraft

Optimal control laws are obtained for the elevator and the ailerons for a modern fighter aircraft in a rolling pullout maneuver. The problem is solved for three flight conditions using the conjugate gradient method.