a b s t r a c tIn this work we briefly discuss some concepts of structural reliability as well as the optimization algorithm that is commonly used in this context, called HLRF. We show that the HLRF algorithm is a particular case of the SQP method, in which the Hessian of the Lagrangian is approximated by an identity matrix. Motivated by this fact, we propose the HLRF-BFGS algorithm that considers the BFGS update formula to approximate the Hessian. The algorithm proposed herein is as simple as the HLRF algorithm, since it requires just one function and gradient evaluation at each iteration and the new iterate is given by a recursive formula. Comparative numerical experiments on a set of problems selected from the literature are presented to illustrate the performance of the algorithm and the results indicate that the HLRF-BFGS algorithm has the advantage of being more robust and efficient with respect to the function and gradient evaluation, than HLRF.

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In this work we discuss global convergence of a general filter algorithm that does not depend neither on the definition of the forbidden region, which can be given by the original or slanting filter rule, nor on the way in which the step is computed. This algorithm basically consists of calculating a point not forbidden by the filter from the current point. Assuming that this step must be efficient, in the sense that, near a feasible non-stationary point the decrease in the objective function is relatively large, we prove the global convergence of the algorithm. We also discuss that such condition is satisfied if the step is computed by the SQP or Inexact Restoration methods. For SQP we present a general proof of this result that is valid as for the original as for the slanting filter criterion. In order to compare the performance of the general filter algorithm according to the method used to calculate the step and the filter rule regarded, we present numerical experiments performed with problems from CUTEr collection.

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Resumo. Neste trabalho propomos duas estratégias de redução de cenários que podem ser aplicadas ao problema de planejamento da operação hidrotérmica do sistema brasileiro de geração de energia elétrica. Este é um problema de decisão sequencial estocástica, cuja solução deve ser não-antecipativa, no sentido de que a decisão em um estágio deve ser tomada sem o conhecimento do futuro. As estratégias propostas estão baseadas no conceito de cenários irrelevantes. A identificação de tais cenários, possibilita a eliminação destes no conjunto original de cenários usados para tratar a estocasticidade do problema, reduzindo assim sua dimensão. A resolução do problema não-antecipativo com a medida de risco CVaR considerando esse conjunto reduzido fornece resultados tão confiáveis quanto aqueles obtidos a partir do conjunto original. Experimentos numéricos são apresentados a fim de ilustrar a aplicação das técnicas propostas considerando um conjunto de dados reais.Palavras-chave. Análise de cenários não-antecipativos, Cenários irrelavantes, Otimização não-linear, Sistemas hidrotérmicos.