A New Preconditioning Approachfor an Interior Point–Proximal Method of Multipliers for Linear and Convex Quadratic Programming

In this paper, we address the efficient numerical solution of linear and quadratic programming problems, often of large scale. With this aim, we devise an infeasible interior point method, blended with the proximal method of multipliers, which in turn results in a primal-dual regularized interior point method. Application of this method gives rise to a sequence of increasingly ill-conditioned linear systems which cannot always be solved by factorization methods, due to memory and CPU time restrictions. We propose a novel preconditioning strategy which is based on a suitable sparsification of the normal equations matrix in the linear case, and also constitutes the foundation of a block-diagonal preconditioner to accelerate MINRES for linear systems arising from the solution of general quadratic programming problems. Numerical results for a range of test problems demonstrate the robustness of the proposed preconditioning strategy, together with its ability to solve linear systems of very large dimension

Concepções de agricultores ecológicos do Paraná sobre alimentação saudável.

OBJETIVO: Descrever as concepções de agricultores ecológicos sobre alimentação saudável. MÉTODOS: Estudo com abordagem qualitativa. Entre janeiro e fevereiro de 2007, foram realizadas entrevistas em profundidade com o apoio de um roteiro com 11 mulheres e um homem residentes em comunidade agrícola de Rio Branco do Sul, PR, selecionados aleatoriamente dentre as 20 famílias de agricultores ecológicos desse município. RESULTADOS: Três categorias de análise foram identificadas: "tomada de consciência da alimentação saudável", "capacidade de compra" e "terra saudável". O significado da alimentação saudável para as mulheres agricultoras envolve a ideia de que os alimentos devem ser naturais, sem agrotóxicos nem produtos químicos industrializados. Cotidianamente o consumo de frutas, verduras e legumes somado ao básico feijão, arroz e carne deve ser abundante e a composição do prato deve visar à prevenção de obesidade e doenças crônico-degenerativas. O cuidado com os recursos naturais para garantir a produção de alimentos saudáveis, a segurança alimentar, a sustentabilidade do meio ambiente e a vida futura do planeta integram o conceito de alimentação saudável. CONCLUSÕES: O conhecimento, a autocrítica e o discernimento acompanharam as concepções em relação à alimentação saudável

Large-scale unit commitment under uncertainty: an updated literature survey

The Unit Commitment problem in energy management aims at finding the optimal production schedule of a set of generation units, while meeting various system-wide constraints. It has always been a large-scale, non-convex, difficult problem, especially in view of the fact that, due to operational requirements, it has to be solved in an unreasonably small time for its size. Recently, growing renewable energy shares have strongly increased the level of uncertainty in the system, making the (ideal) Unit Commitment model a large-scale, non-convex and uncertain (stochastic, robust, chance-constrained) program. We provide a survey of the literature on methods for the Uncertain Unit Commitment problem, in all its variants. We start with a review of the main contributions on solution methods for the deterministic versions of the problem, focussing on those based on mathematical programming techniques that are more relevant for the uncertain versions of the problem. We then present and categorize the approaches to the latter, while providing entry points to the relevant literature on optimization under uncertainty. This is an updated version of the paper "Large-scale Unit Commitment under uncertainty: a literature survey" that appeared in 4OR 13(2), 115--171 (2015); this version has over 170 more citations, most of which appeared in the last three years, proving how fast the literature on uncertain Unit Commitment evolves, and therefore the interest in this subject

A new class of preconditioners for large-scale linear systems from interior point methods for linear programming

A new class of preconditioners for the iterative solution of the linear systems arising from interior point methods is proposed. For many of these methods, the linear systems are symmetric and indefinite. The system can be reduced to a system of normal equations which is positive definite. We show that all preconditioners for the normal equations system have an equivalent for the augmented system while the opposite is not true. The new class of preconditioners works better near a solution of the linear programming problem when the matrices are highly ill conditioned. The preconditioned system can be reduced to a positive definite one. The techniques developed for a competitive implementation are rather sophisticated since the subset of columns is not known a priori. The new preconditioner applied to the conjugate gradient method compares favorably with the Cholesky factorization approach on large-scale problems whose Cholesky factorization contains too many nonzero entries. (C) 2004 Elsevier Inc. All rights reserved.39412

Primal-Dual Interior Point Method Applied to the Short Term Hydroelectric Scheduling Including a Perturbing Parameter

In this work, the primal-dual interior point method is studied and developed to solve the predispatch DC (direct current) problem that minimizes losses in the transmission and costs in the generation of a hydroelectric power system, formulated as a network flow model. The matrix obtained by the application of the interior point method is reduced of such form that the final linear system can be implemented of efficient form. Moreover, a modification of this method is made on the basis of a heuristic that determines a new perturbing parameter. This modified method (VPMPD) showed to be efficient in the practical and achieved convergence in fewer iterations when compared with an existing implementation of the network flow model, that does not take in consideration such perturbing parameter.7553353