Navegando por Palavras-chave "Método De Newton"

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    Um Estudo Sobre O Problema De Empacotamento De Círculos
    (Universidade Federal de São Paulo (UNIFESP), 2018-06-15) Oliveira, Juliana Rodrigues Silva De [UNIFESP]; Senne, Thadeu Alves [UNIFESP]; Universidade Federal de São Paulo (UNIFESP)
    The Packing Problems Consist In Arranging Some Subjects Within A Certain Region. In This Work, We Study A Particular Case Of This Problem: The Problem Of Packing Circular Items, In Which The Items That Has To Be Organized Inside Of A Certain Region Are Unitary Circles. We Considered That The Region That Have Those Items Has One Of These Forms: Circular, Square, Rectangular And Triangular Or Strip (That Is, A Rectangle That Has One Of Two Dimensions Fixed). The Goal Is To Minimize The Dimensions Of The Object So That There Is No Overlap Between Any Two Pairs Of Items And Each Item Is Prevented To Cross The Boundary Of The Object. The Knowledge Of This Class Of Problems Is Essential For The Understanding More About The Complex Problems, Such As Packing Molecules. So, The Study About This Subject Is Relevant. Here, We Solve The Problem Of Packing Circles Using Algencan, That Is A Software Based On The Augmented Lagrangian Method For Nonlinear Optimization Problems, And We Compared The Performance Of The Original
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    Métodos Do Tipo Newton Aplicados A Métodos De Restauração Inexata
    (Universidade Federal de São Paulo (UNIFESP), 2017-03-14) Herrera, Francis Lorena Larreal [UNIFESP]; Bueno, Luis Felipe Cesar Da Rocha [UNIFESP]; Universidade Federal de São Paulo (UNIFESP)
    In this dissertation, we study Brent’s method to solve systems of equations and their relation with Inexata Restoration methods. Brent’s method solves a non-linear system by dividing it into blocks and considering linearizations of these blocks in each iteration. We reconstruct a proof of a theorem in which are established the conditions so that the point sequence generated by Brent’s method has local quadratic convergence to the system solution. Inexact Restoration methods are developed to solved constrained optimization problems and the have the characteristic of dividing each iteration into two phases. In the first one, they seek to improve viability and, in the second, optimality. So, it is natural to think that Inexact Restoration methods look to solve the KKT system by dividing it into two blocks. For this reason, it seems evident the existence of a relation between Brent’s and Inexact Restoration methods. Considering this, we present a quadratic local convergence result for the point sequences generated by the Inexact Restoration methods, derived from adaptations in the convergence demonstration of Brent’s method. After that, we propose two iterative computational methods for optimization, introducing small modifications in the Inexact Restoration method. We show that these two methods also have quadratic convergence and we discuss possible advantages and disadvantages of each one of them. Finally we briefly comment some ideas about how these methods could be inserted into a scheme with global convergence.