Resumo: Este projeto de pesquisa tem como objetivo a concepção, implementação, solução e teste de um modelo de Pré-Despacho de Geração (PDG) para o ambiente de mercados de energia, que supra as deficiências dos modelos de PDG adotados no Brasil. Assim, a abordagem proposta deve introduzir novos aspectos de modelagem, tais como: i) a introdução de aspectos associados aos mercados de energia internamente ao modelo de PDG; ii) a representação das inter-relações entre os mercados pool e bilateral em um único modelo de PDG; iii) a discretização do problema em base horária, possibilitando, de fato, a implementação de um mercado de curtíssimo prazo; iv) a avaliação da função de custo de oportunidade como base para a inserção de objetivos associados à otimização da produção de energia hidráulica no mercado pool / Abstract: This research aims at the conception, implementation, solution and testing of the proposed Short term Generation Scheduling Model (PDG), specific for the energy market environment. This model focuses on the improvement in the dispatch model used by the Brazilian energy sector. The proposed approach introduces brand new modeling aspects, such as: i) the introduction of modeling aspects associated with energy markets into the PDG model; ii) the representation of the interrelation between pool and bilateral markets within a single optimization problem; iii) the discretization of the problem is introduced in an hourly basis aiming at the implementation of an effective short time energy market; iv) the evaluation of the opportunity costs function as a basis for insertion of objectives associated with optimization of hydraulic energy production in pool market / Orientador: Leonardo Nepomuceno / Coorientador: Paulo Sérgio da Silva / Banca: Takaaki Ohishi / Banca: Edmea Cassia Baptista / Mestre

Global optimization methods can be classified into two non-overlapping classes with respect to accuracy: those with guaranteed accuracy and those without. The former are called bounding methods, the latter point methods. Bounding methods compute lower and upper bounds of function over a box and give a lower bound and an upper bound for the minimum. Point methods compute function values at points and output as the minimum the function value at a point. R. E. Moore was the first to propose the bounding method using interval arithmetic for unconstrained global optimization. The first bounding method using interval arithmetic for constrained global optimization was due to E. R. Hansen and S. Sengupta. These methods are the well known bounding methods. Since these methods use interval arithmetic, we call them interval arithmetic methods. This dissertation studies the new bounding methods that use interval constraints, which is called interval constraint methods. We prove that interval constraints is a generalization of interval arithmetic, computing an interval function in interval constraints gives the same result as in interval arithmetic. We propose a hypernarrowing algorithm using interval constraints. This algorithm produces a smaller interval result for the range of function f over a given domain than interval arithmetic. We present a generic Branch-and-Bound algorithm for unconstrained global optimization, prove the properties of the algorithm, and propose improvements on the algorithm. From this algorithm, we can obtain its interval arithmetic version and interval constraint version. We investigate the role of interval constraints in global optimization and discuss the performance and characteristics of interval arithmetic methods and interval constraint ones. Based on the Branch-and-Bound algorithm for unconstrained global optimization, we present a generic Branch-and-Bound algorithm for constrained global optimization, study the effect of Fritz-John conditions as redundant constraints and compare the interval arithmetic method for constrained optimization with the interval constraint one. / Graduate

The theory of ordinary factor analysis and its application by means of software packages do not make provision for data sampled from populations with hierarchical structures. Since data are often obtained from such populations - educational data for example ¬the lack of procedures to analyse data of this kind needs to be addressed. A review of the ordinary factor analysis model and maximum likelihood estimation of the parameters in exploratory and confirmatory models is provided, together with practical applications. Subsequently, the concept of hierarchically structured populations and their models, called multilevel models, are introduced. A general framework for the estimation of the unknown parameters in these models is presented. It contains two estimation procedures. The first is the marginal maximum likelihood method in which an iterative expected maximisation approach is used to obtain the maximum likelihood estimates. The second is the Fisher scoring method which also provides estimated standard errors for the maximum likelihood parameter estimates. For both methods, the theory is presented for unconstrained as well as for constrained estimation. A two-stage procedure - combining the mentioned procedures - is proposed for parameter estimation in practice. Multilevel factor analysis models are introduced next, and subsequently a particular two-level factor analysis model is presented. The general estimation theory that was presented earlier is applied to this model - in exploratory and confirmatory analysis. First, the marginal maximum likelihood method is used to obtain the equations for determining the parameter estimates. It is then shown how an iterative expected max¬imisation algorithm is used to obtain these estimates in unconstrained and constrained optimisation. This method is applied to real life data using a FORTRAN program. Secondly, equations are derived by means of the Fisher scoring method to obtain the maximum likelihood estimates of the parameters in the two-level factor analysis model for exploratory and confirmatory analysis. A FORTRAN program was written to apply this method in practice. Real life data are used to illustrate the method. Finally, flowing from this research, some areas for possible further research are pro¬posed. / Thesis (PhD (Applied Statistics))--University of Pretoria, 2007. / Statistics / unrestricted

In this thesis, we study the stability and its trade-off with optimization error for stochastic gradient descent (SGD) algorithms in the pairwise learning setting. Pairwise learning refers to a learning task which involves a loss function depending on pairs of instances among which notable examples are bipartite ranking, metric learning, area under ROC curve (AUC) maximization and minimum error entropy (MEE) principle. Our contribution is twofold. Firstly, we establish the stability results for SGD for pairwise learning in the convex, strongly convex and non-convex settings, from which generalization errors can be naturally derived. Moreover, we also give the stability results of buffer-based SGD and projected SGD. Secondly, we establish the trade-off between stability and optimization error of SGD algorithms for pairwise learning. This is achieved by lower-bounding the sum of stability and optimization error by the minimax statistical error over a prescribed class of pairwise loss functions. From this fundamental trade-off, we obtain lower bounds for the optimization error of SGD algorithms and the excess expected risk over a class of pairwise losses. In addition, we illustrate our stability results by giving some specific examples and experiments of AUC maximization and MEE.

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