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Otimização da programação da manutenção dos ativos de transmissão do sistema elétrico brasileiro considerando penalidades por indisponibilidade, restrições sistêmicas e logística das equipes técnicas; Optimization of maintenance programming of transmission assets of the brazilian electric power system considering penalties for unavailability, systemic constraints and logistics technical teams

José Evangelista Araujo Neto
Fonte: Biblioteca Digital da Unicamp Publicador: Biblioteca Digital da Unicamp
Tipo: Dissertação de Mestrado Formato: application/pdf
Publicado em 14/10/2011 PT
Relevância na Pesquisa
45.95%
Uma empresa de energia elétrica tem por obrigação garantir a continuidade e a qualidade do serviço prestado. A fim de incentivar a qualidade do serviço, a ANEEL introduziu penalidades nos contratos com as concessionárias de serviços públicos de transmissão de energia elétrica caso as instalações de transmissão sejam desligadas, por acidente, falha de equipamento ou manutenção programada. Abordagens tradicionais de manutenção em sistemas de transmissão de energia elétrica se baseiam em ações realizadas periodicamente, ou programadas, de acordo com uma análise de necessidades. Embora essas abordagens tenham o objetivo de melhorar o desempenho destes sistemas, geralmente não há uma avaliação precisa do impacto das ações de manutenção na confiabilidade dos mesmos relacionada aos recursos empregados, bem como penalidades legais decorrentes. O objeto assim formulado caracteriza-se como um problema de otimização combinatória com o objetivo de encontrar o encadeamento das ações de manutenções que minimizem os recursos utilizados em manutenções e garanta um nível de confiabilidade desejado para o Sistema Elétrico. Este trabalho propõe uma abordagem para enfrentar este problema baseada na relação confiabilidade/custo com a perspectiva de encontrar as melhores estratégias para a realização de manutenções em equipamentos (ativos) de transmissão de energia elétrica...

A sequential quadratic programming algorithm using an incomplete solution of the subproblem

Murray, Walter; Prieto, Francisco J.
Fonte: Society for Industrial and Applied Mathematics Publicador: Society for Industrial and Applied Mathematics
Tipo: info:eu-repo/semantics/publishedVersion; info:eu-repo/semantics/article Formato: application/pdf
Publicado em /08/1995 ENG
Relevância na Pesquisa
45.9%
We analyze sequential quadratic programming (SQP) methods to solve nonlinear constrained optimization problems that are more flexible in their definition than standard SQP methods. The type of flexibility introduced is motivated by the necessity to deviate from the standard approach when solving large problems. Specifically we no longer require a minimizer of the QP subproblem to be determined or particular Lagrange multiplier estimates to be used. Our main focus is on an SQP algorithm that uses a particular augmented Lagrangian merit function. New results are derived for this algorithm under weaker conditions than previously assumed; in particular, it is not assumed that the iterates lie on a compact set; This research was supported by National Science Foundation grant DDMo9204208, Department of Energy grant DE-FG03-92ER25117, Office of Naval Research grant N00014-90-J-1242, and the Bank of Spain

Estudos em programação linear; Studies in linear programming

Adão Nascimento dos Passos
Fonte: Biblioteca Digital da Unicamp Publicador: Biblioteca Digital da Unicamp
Tipo: Dissertação de Mestrado Formato: application/pdf
Publicado em 16/10/2009 PT
Relevância na Pesquisa
46.08%
Neste trabalho é feito um estudo sobre Programação Linear e um texto sobre alguns de seus assuntos básicos, construído com uma linguagem didática, visando sua utilização em sala de aula. São apresentados alguns problemas lineares, os fundamentos matemáticos da Programação Linear e o método Simplex, finalizando com um estudo do princípio da decomposição de Dantzig-Wolfe, que é um procedimento para a resolução de problemas lineares de grande porte e com estrutura especial.; In this work we have done a study on Linear Programming and a text with some basic issues, using a didactic language, and aiming its utilization in the classroom. Some linear problems are shown here, the mathematical background of Linear Programming and the Simplex method. Finaly, we have also presented a study on the principle of Dantzig-Wolfe's decomposition, which is a procedure for solving large linear problems with special structure.

A matematica no projeto Ciencia na Escola : a busca da autonomia dos alunos; The mathematics in the project Science in the School : the seacrch for the autonomy of students

Claudinei de Camargo Sant'Ana
Fonte: Biblioteca Digital da Unicamp Publicador: Biblioteca Digital da Unicamp
Tipo: Tese de Doutorado Formato: application/pdf
Publicado em 20/02/2008 PT
Relevância na Pesquisa
36.07%
O presente trabalho foi desenvolvido em uma escola pertencente à rede pública do ensino fundamental, no período compreendido entre 1997 e 2004, os trabalhos foram mediados pelo grupo de professores e alunos em ação colaborativa, fundamentado nos princípios pedagógicos do "Projeto Ciência na Escola". As ações ocorreram, em dois momentos norteadores, que marcaram significativamente a prática de sala de aula. A pesquisa qualitativa, em seu desenvolvimento quanto ao trabalho de campo, foi caracterizada como pesquisaação, desenvolvida junto aos alunos e professores, utilizando os procedimentos da Metodologia da Pesquisa Científica, segundo a reelaboração desenvolvida pelo grupo colaborativo de professores. A análise qualitativa foi desenvolvida baseada no recorte do material produzido, por professores e alunos. Nesta análise, que consideramos também como uma pesquisa-ação, aprofundamo-nos na discussão do desenvolvimento dos trabalhos de pesquisa; as mudanças de postura; o desenvolvimento da autonomia. A produção matemática dos alunos foi baseada na Modelagem Matemática via Programação Dinâmica, com o propósito da melhoria do fazer pedagógico. Os resultados demonstram a possibilidade de se constituir um grupo de professores pesquisadores e alunos também pesquisadores na escola pública...

Algebraic Functions, Computer Programming, and the Challenge of Transfer

Schanzer, Emmanuel Tanenbaum
Fonte: Harvard University Publicador: Harvard University
Tipo: Thesis or Dissertation; text Formato: application/pdf
EN
Relevância na Pesquisa
36.18%
Students' struggles with algebra are well documented. Prior to the introduction of functions, mathematics is typically focused on applying a set of arithmetic operations to compute an answer. The introduction of functions, however, marks the point at which mathematics begins to focus on building up abstractions as a way to solve complex problems. A common refrain about word problems is that “the equations are easy to solve - the hard part is setting them up!” A student of algebra is asked to identify functional relationships in the world around them - to set up the equations that describe a system- and to reason about these relationships. Functions, in essence, mark the shift from computing answers to solving problems. Researchers have called for this shift to accompany a change in pedagogy, and have looked to computer programming and game design as a means to combine mathematical rigor with creative inquiry. Many studies have explored the impact of teaching students to program, with the goal of having them transfer what they have learned back into traditional mathematics. While some of these studies have shown positive outcomes for concepts like geometry and fractions, transfer between programming and algebra has remained elusive. The literature identifies a number of conditions that must be met to facilitate transfer...

N-fold integer programming in cubic time

Hemmecke, Raymond; Onn, Shmuel; Romanchuk, Lyubov
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 17/01/2011
Relevância na Pesquisa
36.12%
N-fold integer programming is a fundamental problem with a variety of natural applications in operations research and statistics. Moreover, it is universal and provides a new, variable-dimension, parametrization of all of integer programming. The fastest algorithm for $n$-fold integer programming predating the present article runs in time $O(n^{g(A)}L)$ with $L$ the binary length of the numerical part of the input and $g(A)$ the so-called Graver complexity of the bimatrix $A$ defining the system. In this article we provide a drastic improvement and establish an algorithm which runs in time $O(n^3 L)$ having cubic dependency on $n$ regardless of the bimatrix $A$. Our algorithm can be extended to separable convex piecewise affine objectives as well, and also to systems defined by bimatrices with variable entries. Moreover, it can be used to define a hierarchy of approximations for any integer programming problem.

The bipartite unconstrained 0-1 quadratic programming problem: polynomially solvable cases

Punnen, Abraham P.; Sripratak, Piyashat; Karapetyan, Daniel
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
36.12%
We consider the bipartite unconstrained 0-1 quadratic programming problem (BQP01) which is a generalization of the well studied unconstrained 0-1 quadratic programming problem (QP01). BQP01 has numerous applications and the problem is known to be MAX SNP hard. We show that if the rank of an associated $m\times n$ cost matrix $Q=(q_{ij})$ is fixed, then BQP01 can be solved in polynomial time. When $Q$ is of rank one, we provide an $O(n\log n)$ algorithm and this complexity reduces to $O(n)$ with additional assumptions. Further, if $q_{ij}=a_i+b_j$ for some $a_i$ and $b_j$, then BQP01 is shown to be solvable in $O(mn\log n)$ time. By restricting $m=O(\log n),$ we obtain yet another polynomially solvable case of BQP01 but the problem remains MAX SNP hard if $m=O(\sqrt[k]{n})$ for a fixed $k$. Finally, if the minimum number of rows and columns to be deleted from $Q$ to make the remaining matrix non-negative is $O(\log n)$ then we show that BQP01 polynomially solvable but it is NP-hard if this number is $O(\sqrt[k]{n})$ for any fixed $k$. Keywords: quadratic programming, 0-1 variables, polynomial algorithms, complexity, pseudo-Boolean programming.; Comment: 20 pages

Linear Programming Formulation of the Boolean Satisfiability Problem

Diaby, Moustapha
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
36.09%
Theorem 38 and Corollary 39 are in error. The modeling idea is sound, but it needs 9-dimensional z-variables instead of the 8-dimensional variables defined in notations 24.1. Examples of the correct model (with 9-index variables) are: (1) Diaby, M., "Linear Programming Formulation of the Set Partitioning Problem," International Journal of Operational Research 8:4 (August 2010) pp. 399-427; (2) Diaby, M., "Linear Programming Formulation of the Vertex Coloring Problem," International Journal of Mathematics in Operational Research 2:3 (May 2010) pp. 259-289; (3) Diaby, M., "The Traveling Salesman Problem: A Linear Programming Formulation," WSEAS Transactions on Mathematics, 6:6 (June 2007) pp. 745-754.; Comment: This paper has been withdrawn because Theorem 38 and Corollary 39 are in error. The modeling needs 9-dimensional z-variables instead of the 8-dimensional variables defined in notations 24.1

MM Algorithms for Geometric and Signomial Programming

Lange, Kenneth; Zhou, Hua
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 14/07/2010
Relevância na Pesquisa
36.1%
This paper derives new algorithms for signomial programming, a generalization of geometric programming. The algorithms are based on a generic principle for optimization called the MM algorithm. In this setting, one can apply the geometric-arithmetic mean inequality and a supporting hyperplane inequality to create a surrogate function with parameters separated. Thus, unconstrained signomial programming reduces to a sequence of one-dimensional minimization problems. Simple examples demonstrate that the MM algorithm derived can converge to a boundary point or to one point of a continuum of minimum points. Conditions under which the minimum point is unique or occurs in the interior of parameter space are proved for geometric programming. Convergence to an interior point occurs at a linear rate. Finally, the MM framework easily accommodates equality and inequality constraints of signomial type. For the most important special case, constrained quadratic programming, the MM algorithm involves very simple updates.; Comment: 16 pages, 1 figure

Theory and Applications of N-Fold Integer Programming

Onn, Shmuel
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
36.09%
We overview our recently introduced theory of n-fold integer programming which enables the polynomial time solution of fundamental linear and nonlinear integer programming problems in variable dimension. We demonstrate its power by obtaining the first polynomial time algorithms in several application areas including multicommodity flows and privacy in statistical databases.; Comment: IMA Volume on Mixed Integer Nonlinear Programming, Frontier Series, Springer, to appear

Shrink-Wrapping trajectories for Linear Programming

Zinchenko, Yuriy
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 30/05/2010
Relevância na Pesquisa
36.1%
Hyperbolic Programming (HP) --minimizing a linear functional over an affine subspace of a finite-dimensional real vector space intersected with the so-called hyperbolicity cone-- is a class of convex optimization problems that contains well-known Linear Programming (LP). In particular, for any LP one can readily provide a sequence of HP relaxations. Based on these hyperbolic relaxations, a new Shrink-Wrapping approach to solve LP has been proposed by Renegar. The resulting Shrink-Wrapping trajectories, in a sense, generalize the notion of central path in interior-point methods. We study the geometry of Shrink-Wrapping trajectories for Linear Programming. In particular, we analyze the geometry of these trajectories in the proximity of the so-called central line, and contrast the behavior of these trajectories with that of the central path for some pathological LP instances. In addition, we provide an elementary proof of convexity of hyperbolicity cones over reals.; Comment: Keywords: Hyperbolic polynomials; hyperbolicity cones; hyperbolic programming; linear programming; Shrink-Wrapping

A New Algorithm for Linear Programming

Mehendale, Dhananjay P.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
36.12%
In this paper we propose two types of new algorithms for linear programming. The first type of these new algorithms uses algebraic methods while the second type of these new algorithms uses geometric methods. The first type of algorithms is based on treating the objective function as a parameter. In this method, we form a matrix using coefficients in the system of equations consisting objective equation and equations obtained from inequalities defining constraint by introducing slack/surplus variables. We obtain reduced row echelon form for this matrix containing only one variable, namely, the objective function itself as an unknown parameter. We analyse this matrix in the reduced row echelon form and develop a clear cut method to find the optimal solution for the problem at hand, if and when it exists. We see that the entire optimization process can be developed through the proper analysis of the said matrix in the reduced row echelon form. The second type of algorithms that we propose for linear programming are inspired by geometrical considerations. All these algorithms pursue common aim of approaching closer and closer to centroid or some centrally located interior point for speeding up the process of reaching an optimal solution! We then proceed to show that the algebraic method developed above for linear programming naturally extends to non-linear and integer programming problems. For non-linear and integer programming problems we use the technique of Grobner bases and the methods of solving linear Diophantine equations respectively.; Comment: 53 Pages. Revised Section 2 by adding new geometry based algorithms for linear programming

Path Following in the Exact Penalty Method of Convex Programming

Zhou, Hua; Lange, Kenneth
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 17/01/2012
Relevância na Pesquisa
36.1%
Classical penalty methods solve a sequence of unconstrained problems that put greater and greater stress on meeting the constraints. In the limit as the penalty constant tends to $\infty$, one recovers the constrained solution. In the exact penalty method, squared penalties are replaced by absolute value penalties, and the solution is recovered for a finite value of the penalty constant. In practice, the kinks in the penalty and the unknown magnitude of the penalty constant prevent wide application of the exact penalty method in nonlinear programming. In this article, we examine a strategy of path following consistent with the exact penalty method. Instead of performing optimization at a single penalty constant, we trace the solution as a continuous function of the penalty constant. Thus, path following starts at the unconstrained solution and follows the solution path as the penalty constant increases. In the process, the solution path hits, slides along, and exits from the various constraints. For quadratic programming, the solution path is piecewise linear and takes large jumps from constraint to constraint. For a general convex program, the solution path is piecewise smooth, and path following operates by numerically solving an ordinary differential equation segment by segment. Our diverse applications to a) projection onto a convex set...

Guaranteed Accuracy for Conic Programming Problems in Vector Lattices

Jansson, Christian
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 30/07/2007
Relevância na Pesquisa
36.08%
This paper presents rigorous forward error bounds for linear conic optimization problems. The error bounds are formulated in a quite general framework; the underlying vector spaces are not required to be finite-dimensional, and the convex cones defining the partial ordering are not required to be polyhedral. In the case of linear programming, second order cone programming, and semidefinite programming specialized formulas are deduced yielding guaranteed accuracy. All computed bounds are completely rigorous because all rounding errors due to floating point arithmetic are taken into account. Numerical results, applications and software for linear and semidefinite programming problems are described.

Semidefinite programming and eigenvalue bounds for the graph partition problem

van Dam, Edwin R.; Sotirov, Renata
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
36.08%
The graph partition problem is the problem of partitioning the vertex set of a graph into a fixed number of sets of given sizes such that the sum of weights of edges joining different sets is optimized. In this paper we simplify a known matrix-lifting semidefinite programming relaxation of the graph partition problem for several classes of graphs and also show how to aggregate additional triangle and independent set constraints for graphs with symmetry. We present an eigenvalue bound for the graph partition problem of a strongly regular graph, extending a similar result for the equipartition problem. We also derive a linear programming bound of the graph partition problem for certain Johnson and Kneser graphs. Using what we call the Laplacian algebra of a graph, we derive an eigenvalue bound for the graph partition problem that is the first known closed form bound that is applicable to any graph, thereby extending a well-known result in spectral graph theory. Finally, we strengthen a known semidefinite programming relaxation of a specific quadratic assignment problem and the above-mentioned matrix-lifting semidefinite programming relaxation by adding two constraints that correspond to assigning two vertices of the graph to different parts of the partition. This strengthening performs well on highly symmetric graphs when other relaxations provide weak or trivial bounds.

A O(n^8) X O(n^7) Linear Programming Model of the Quadratic Assignment Problem

Diaby, Moustapha
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
36.09%
This paper has been withdrawn because Theorem 21 and Corollary 22 are in error; The modeling idea is OK, but it needs 9-dimensional variables instead of the 8-dimensional variables defined in notations 6.9. Examples of the correct model (with 9-index variables) are: (1) Diaby, M., "Linear Programming Formulation of the Set Partitioning Problem," International Journal of Operational Research 8:4 (August 2010) pp. 399-427; (2) Diaby, M., "Linear Programming Formulation of the Vertex Coloring Problem," International Journal of Mathematics in Operational Research 2:3 (May 2010) pp. 259-289; (3) Diaby, M., "The Traveling Salesman Problem: A Linear Programming Formulation," WSEAS Transactions on Mathematics, 6:6 (June 2007) pp. 745-754.; Comment: Theorem 21 and Corollary 22 are in error; The modeling needs 9-dimensional variables instead of the 8-dimensional variables defined in notations 6.9

A O(n^8) X O(n^7) Linear Programming Model of the Traveling Salesman Problem

Diaby, Moustapha
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
36.09%
This paper has been withdrawn because Theorem 25 and Corollary 26 are incorrect. The modeling idea is OK but it needs 9-dimensional variables instead of the 8-dimensional variables defined in notations 10.2. Examples of the correct model (with 9-index variables) are: (1) Diaby, M., "Linear Programming Formulation of the Set Partitioning Problem," International Journal of Operational Research 8:4 (August 2010) pp. 399-427; (2) Diaby, M., "Linear Programming Formulation of the Vertex Coloring Problem," International Journal of Mathematics in Operational Research 2:3 (May 2010) pp. 259-289; (3) Diaby, M., "The Traveling Salesman Problem: A Linear Programming Formulation," WSEAS Transactions on Mathematics, 6:6 (June 2007) pp. 745-754.; Comment: Theorem 25 and Corollary 26 are incorrect. The modeling needs 9-dimensional variables instead of the 8-dimensional variables defined in notations 10.2

Mixed-integer Quadratic Programming is in NP

Del Pia, Alberto; Dey, Santanu S.; Molinaro, Marco
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 17/07/2014
Relevância na Pesquisa
36.1%
Mixed-integer quadratic programming is the problem of optimizing a quadratic function over points in a polyhedral set where some of the components are restricted to be integral. In this paper, we prove that the decision version of mixed-integer quadratic programming is in NP, thereby showing that it is NP-complete. This is established by showing that if the decision version of mixed-integer quadratic programming is feasible, then there exists a solution of polynomial size. This result generalizes and unifies classical results that quadratic programming is in NP and integer linear programming is in NP.

English language & third generation programming language pedagogical practice analysis

Falbo, Vincent
Fonte: Rochester Instituto de Tecnologia Publicador: Rochester Instituto de Tecnologia
Tipo: Tese de Doutorado
EN_US
Relevância na Pesquisa
36.09%
In an effort to provide better computer programming instruction to more students at an introductory level, pedagogical methods could be improved using a paradigm of instruction based on the same strategies used to teach students spoken languages. Although many different methodologies of instruction have been explored in the past, this document identifies relationships between spoken languages and computer languages that encourage the exploration of the best practices of teaching English Language Arts so that they could be applied to computer programming instruction. Those with backgrounds in mathematics and science initially completed programming tasks. Much literature about the problem solving aspects of programming is available; however, the researcher of this document found it difficult to obtain literature about the opportunities for growth provided by the humanities. This research is an attempt to foster the programming skills of students based on language skills. Given the similarities between spoken languages and object-oriented programming languages that have emerged, there is much encouragement that there may be possibilities for a new instructional paradigm. Following is an analysis of how computer languages are taught and how English is taught...

The problem with integer programming

Williams, H. Paul
Fonte: Oxford University Press on behalf of the Institute of Mathematics and its Applications Publicador: Oxford University Press on behalf of the Institute of Mathematics and its Applications
Tipo: Article; PeerReviewed Formato: application/pdf
Publicado em //2011 EN; EN
Relevância na Pesquisa
46.07%
Integer programming (IP), also known as discrete optimization, is a way of modelling a very wide range of problems involving indivisibilities (e.g. yes/no investment decisions) and non-convexities (e.g. economies of scale and fixed cost allocation). Such problems arise in many areas; these are mentioned in the paper. However, IP demands ingenuity in both building models and in their solution. Much is still not properly understood. This paper investigates the question: ‘Is IP like Linear Programming (LP)? ’ The mathematical and economic properties of IP will be contrasted with LP. It will be suggested that the mathematics and economics of IP are still not properly understood. Many of the results which apply to LP do not apply to IP. It will be asserted that this lack of understanding reveals inadequacies in both the mathematics and economics. Published online October 5th, 2010.