Reformulation of variational inequalities on a simplex and compactification of complementarity problems

Many variational inequality problems (VIPs) can be reduced, by a compactification procedure, to a VIP on the canonical simplex. Reformulations of this problem are studied, including smooth reformulations with simple constraints and unconstrained reformulations based on the penalized Fischer-Burmeister function. It is proved that bounded level set results hold for these reformulations under quite general assumptions on the operator. Therefore, it can be guaranteed that minimization algorithms generate bounded sequences and, under monotonicity conditions, these algorithms necessarily nd solutions of the original problem. Some numerical experiments are presented.

The reformulation of nonlinear complementarity problems using the Fischer-Burmeister function

A bounded-level-set result for a reformulation of the box-constrained variational inequality problem proposed recently by Facchinei, Fischer and Kanzow is proved. An application of this result to the (unbounded) nonlinear complementarity problem is suggested. © 1999 Elsevier Science Ltd. All rights reserved.

Reformulation and a Lagrangian heuristic for lot sizing problem on parallel machines

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

A correção como procedimento de reformulação em chat educacional escrito em espanhol por brasileiros: tipos de operacionalização e marcas

O objetivo deste artigo foi analisar, nas interações realizadas por escrito dentro de um chat educacional, os tipos de operacionalização para o processo da correção - enquanto procedimento de reformulação, de acordo com a Perspectiva Textual-Interativa. O corpus, constituído por 31 sessões e por 17 participantes (1 professor e 16 alunos), mostrou a presença de quatro tipos de operacionalização da correção: autocorreção autoiniciada, autocorreção heteroiniciada, heterocorreção autoiniciada e heterocorreção heteroiniciada. O maior número de ocorrências foi o da autocorreção autoiniciada. Esse resultado sugere que: i) os participantes, nesse contexto, parecem se preocupar em preservar a auto-imagem, já que a correção não era essencial à compreensão do texto; ii) os escreventes conhecem as regras e, por isso, se monitoram; iii) a própria ferramenta chat contribui para a autocorreção autoiniciada; e iv) a preferência pela autocorreção autoiniciada parece evitar que o professor assuma o papel de corretor do curso de língua. Foram identificados, ainda, padrões de reformulação com e sem marcadores inscritos na materialidade do texto.

A organização do conhecimento arquivístico: perspectivas de renovação a partir das abordagens científicas canadenses

Desde o final do século XX, as novas formas de produção documental e as novas tecnologias de informação apresentadas à Arquivística têm levado os profissionais da informação a repensar os conceitos e princípios arquivísticos postulados nos antigos manuais da área. Nesse contexto, destaca-se a produção arquivística canadense, que transformou o país em solo fértil para as discussões que circundam a disciplina na contemporaneidade, representando muito bem as necessidades colocadas pelos novos meios de produção documental aos arquivistas na sociedade da informação, redescobrindo princípios e (re) definindo conceitos, métodos e critérios para a criação, manutenção e uso de documentos em meio tradicional e eletrônico. Foi notadamente na década de 1980, que um novo paradigma se enunciou na área e, a partir dele, três correntes emergiram: a Arquivística Integrada - enunciada pela Escola de Québec - que propõe a reintegração da disciplina por meio do ciclo vital dos documentos e uma possível aproximação com a Ciência da Informação, graças à incorporação do termo informação orgânica registrada, como substituição ao termo documento de arquivo; a Arquivística Funcional ou Pós-Moderna, enunciada por Terry Cook - que propõe uma renovação e reformulação dos princípios e conceitos originais da disciplina, adotando a corrente Pós-moderna como pano de fundo; e a Diplomática Arquivística, enunciada primeiramente na Itália por Paola Carucci, mas desenvolvida e reformulada na América do Norte por Luciana Duranti, que busca, por meio do estudo da Diplomática, estabelecer critérios para a crítica textual dos documentos contemporâneos, garantindo ao método diplomático um posto fundamental na Arquivística contemporânea. A vista de tais aspectos, analisa-se, comparativamente, o universo epistemológico dessas três abordagens arquivísticas canadenses, enquanto perspectivas emergentes para a construção de uma disciplina contemporânea, capaz de dar conta dos novos processos de produção, organização e uso da informação orgânica registrada.

Quantization rules for bound states in quantum wells

An algebraic reformulation of the Bohr-Sommerfeld (BS) quantization rule is suggested and applied to the study of bound states in one-dimensional quantum wells. The energies obtained with the present quantization rule are compared to those obtained with the usual BS and WKB quantization rules and with the exact solution of the Schrodinger equation. We find that, in diverse cases of physical interest in molecular physics, the present quantization rule not only yields a good approximation to the exact solution of the Schrodinger equation, but yields more precise energies than those obtained with the usual BS and/or WKB quantization rules. Among the examples considered numerically are the Poeschl-Teller potential and several anharmonic oscillator potentials. which simulate molecular vibrational spectra and the problem of an isolated quantum well structure subject to an external electric field.

Soliton parameters and chaotic sets

In this work we apply a nonperturbative approach to analyze soliton bifurcation ill the presence of surface tension, which is a reformulation of standard methods based on the reversibility properties of the system. The hypothesis is non-restrictive and the results can be extended to a much wider variety of systems. The usual idea of tracking intersections of unstable manifolds with some invariant set is again used, but reversibility plays an important role establishing in a geometrical point of view some kind of symmetry which, in a classical way, is unknown or nonexistent. Using a computer program we determine soliton solutions and also their bifurcations ill the space of parameters giving a picture of the chaotic structural distribution to phase and amplitude shift phenomena. (C) 2009 Published by Elsevier Ltd.

A Lagrangian bound for many-to-many assignment problems

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

On the regularization of mixed complementarity problems

A variational inequality problem (VIP) satisfying a constraint qualification can be reduced to a mixed complementarity problem (MCP). Monotonicity of the VIP implies that the MCP is also monotone. Introducing regularizing perturbations, a sequence of strictly monotone mixed complementarity problems is generated. It is shown that, if the original problem is solvable, the sequence of computable inexact solutions of the strictly monotone MCP's is bounded and every accumulation point is a solution. Under an additional condition on the precision used for solving each subproblem, the sequence converges to the minimum norm solution of the MCP. Copyright © 2000 by Marcel Dekker, Inc.

On the solution of bounded and unbounded mixed complementarity problems

A reformulation of the bounded mixed complementarity problem is introduced. It is proved that the level sets of the objective function are bounded and, under reasonable assumptions, stationary points coincide with solutions of the original variational inequality problem. Therefore, standard minimization algorithms applied to the new reformulation must succeed. This result is applied to the compactification of unbounded mixed complementarity problems. © 2001 OPA (Overseas Publishers Association) N.V. Published by license under the Gordon and Breach Science Publishers imprint, a member of the Taylor & Francis Group.

On the solution of mathematical programming problems with equilibrium constraints

Mathematical programming problems with equilibrium constraints (MPEC) are nonlinear programming problems where the constraints have a form that is analogous to first-order optimality conditions of constrained optimization. We prove that, under reasonable sufficient conditions, stationary points of the sum of squares of the constraints are feasible points of the MPEC. In usual formulations of MPEC all the feasible points are nonregular in the sense that they do not satisfy the Mangasarian-Fromovitz constraint qualification of nonlinear programming. Therefore, all the feasible points satisfy the classical Fritz-John necessary optimality conditions. In principle, this can cause serious difficulties for nonlinear programming algorithms applied to MPEC. However, we show that most feasible points do not satisfy a recently introduced stronger optimality condition for nonlinear programming. This is the reason why, in general, nonlinear programming algorithms are successful when applied to MPEC.

Reformulação para um problema integrado de dimensionamento e sequenciamento de lotes

In this paper, some new constraints and an extended formulation are presented for a Lot Sizing and Scheduling Model proposed in the literature. In the production process considered a key material is prepared and is transformed into different final items. The sequencing decisions are related to the order in which the materials are processed and the lot sizing decisions are related to the final items production. The mathematical formulation considers sequence-dependent setup costs and times. Results of the computational tests executed using the software Cplex 10.0 showed that the performance of the branch-and-cut method can be improved by the proposed a priori reformulation.

A priori reformulations for joint rolling-horizon scheduling of materials processing and lot-sizing problem

In many production processes, a key material is prepared and then transformed into different final products. The lot sizing decisions concern not only the production of final products, but also that of material preparation in order to take account of their sequence-dependent setup costs and times. The amount of research in recent years indicates the relevance of this problem in various industrial settings. In this paper, facility location reformulation and strengthening constraints are newly applied to a previous lot-sizing model in order to improve solution quality and computing time. Three alternative metaheuristics are used to fix the setup variables, resulting in much improved performance over previous research, especially regarding the use of the metaheuristics for larger instances. © 2013 Elsevier Ltd. All rights reserved.

Modelos matemáticos para o problema integrado de dimensionamento de lotes e corte de estoque undimensional

Pós-graduação em Matemática - IBILCE

Limitantes inferiores par ao problema de dimensionamento de lotes em máquinas paralelas

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)