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11 
A value estimation approach to IriImai's method for constrained convex optimization.January 2002 (has links)
Lam Sze Wan. / Thesis (M.Phil.)Chinese University of Hong Kong, 2002. / Includes bibliographical references (leaves 9395). / Abstracts in English and Chinese. / Chapter 1  Introduction  p.1 / Chapter 2  Background  p.4 / Chapter 3  Review of IriImai Algorithm for Convex Programming Prob lems  p.10 / Chapter 3.1  IriImai Algorithm for Convex Programming  p.11 / Chapter 3.2  Numerical Results  p.14 / Chapter 3.2.1  Linear Programming Problems  p.15 / Chapter 3.2.2  Convex Quadratic Programming Problems with Linear Inequality Constraints  p.17 / Chapter 3.2.3  Convex Quadratic Programming Problems with Con vex Quadratic Inequality Constraints  p.18 / Chapter 3.2.4  Summary of Numerical Results  p.21 / Chapter 3.3  Chapter Summary  p.22 / Chapter 4  Value Estimation Approach to IriImai Method for Con strained Optimization  p.23 / Chapter 4.1  Value Estimation Function Method  p.24 / Chapter 4.1.1  Formulation and Properties  p.24 / Chapter 4.1.2  Value Estimation Approach to IriImai Method  p.33 / Chapter 4.2  "A New Smooth Multiplicative Barrier Function Φθ+,u"  p.35 / Chapter 4.2.1  Formulation and Properties  p.35 / Chapter 4.2.2  "Value Estimation Approach to IriImai Method by Us ing Φθ+,u"  p.41 / Chapter 4.3  Convergence Analysis  p.43 / Chapter 4.4  Numerical Results  p.46 / Chapter 4.4.1  Numerical Results Based on Algorithm 4.1  p.46 / Chapter 4.4.2  Numerical Results Based on Algorithm 4.2  p.50 / Chapter 4.4.3  Summary of Numerical Results  p.59 / Chapter 4.5  Chapter Summary  p.60 / Chapter 5  Extension of Value Estimation Approach to IriImai Method for More General Constrained Optimization  p.61 / Chapter 5.1  Extension of IriImai Algorithm 3.1 for More General Con strained Optimization  p.62 / Chapter 5.1.1  Formulation and Properties  p.62 / Chapter 5.1.2  Extension of IriImai Algorithm 3.1  p.63 / Chapter 5.2  Extension of Value Estimation Approach to IriImai Algo rithm 4.1 for More General Constrained Optimization  p.64 / Chapter 5.2.1  Formulation and Properties  p.64 / Chapter 5.2.2  Value Estimation Approach to IriImai Method  p.67 / Chapter 5.3  Extension of Value Estimation Approach to IriImai Algo rithm 4.2 for More General Constrained Optimization  p.69 / Chapter 5.3.1  Formulation and Properties  p.69 / Chapter 5.3.2  Value Estimation Approach to IriImai Method  p.71 / Chapter 5.4  Numerical Results  p.72 / Chapter 5.4.1  Numerical Results Based on Algorithm 5.1  p.73 / Chapter 5.4.2  Numerical Results Based on Algorithm 5.2  p.76 / Chapter 5.4.3  Numerical Results Based on Algorithm 5.3  p.78 / Chapter 5.4.4  Summary of Numerical Results  p.86 / Chapter 5.5  Chapter Summary  p.87 / Chapter 6  Conclusion  p.88 / Bibliography  p.93 / Chapter A  Search Directions  p.96 / Chapter A.1  Newton's Method  p.97 / Chapter A.1.1  Golden Section Method  p.99 / Chapter A.2  Gradients and Hessian Matrices  p.100 / Chapter A.2.1  Gradient of Φθ(x)  p.100 / Chapter A.2.2  Hessian Matrix of Φθ(x)  p.101 / Chapter A.2.3  Gradient of Φθ(x)  p.101 / Chapter A.2.4  Hessian Matrix of φθ (x)  p.102 / Chapter A.2.5  Gradient and Hessian Matrix of Φθ(x) in Terms of ∇xφθ (x) and∇2xxφθ (x)  p.102 / Chapter A.2.6  "Gradient of φθ+,u(x)"  p.102 / Chapter A.2.7  "Hessian Matrix of φθ+,u(x)"  p.103 / Chapter A.2.8  "Gradient and Hessian Matrix of Φθ+,u(x) in Terms of ∇xφθ+,u(x)and ∇2xxφθ+,u(x)"  p.103 / Chapter A.3  Newton's Directions  p.103 / Chapter A.3.1  Newton Direction of Φθ (x) in Terms of ∇xφθ (x) and ∇2xxφθ(x)  p.104 / Chapter A.3.2  "Newton Direction of Φθ+,u(x) in Terms of ∇xφθ+,u(x) and ∇2xxφθ,u(x)"  p.104 / Chapter A.4  Feasible Descent Directions for the Minimization Problems (Pθ) and (Pθ+)  p.105 / Chapter A.4.1  Feasible Descent Direction for the Minimization Prob lems (Pθ)  p.105 / Chapter A.4.2  Feasible Descent Direction for the Minimization Prob lems (Pθ+)  p.107 / Chapter B  Randomly Generated Test Problems for Positive Definite Quadratic Programming  p.109 / Chapter B.l  Convex Quadratic Programming Problems with Linear Con straints  p.110 / Chapter B.l.1  General Description of Test Problems  p.110 / Chapter B.l.2  The Objective Function  p.112 / Chapter B.l.3  The Linear Constraints  p.113 / Chapter B.2  Convex Quadratic Programming Problems with Quadratic In equality Constraints  p.116 / Chapter B.2.1  The Quadratic Constraints  p.117

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A lagrangian reconstruction of a class of local search methods.January 1998 (has links)
by Choi Mo Fung Kenneth. / Thesis (M.Phil.)Chinese University of Hong Kong, 1998. / Includes bibliographical references (leaves 105112). / Abstract also in Chinese. / Chapter 1  Introduction  p.1 / Chapter 1.1  Constraint Satisfaction Problems  p.2 / Chapter 1.2  Constraint Satisfaction Techniques  p.2 / Chapter 1.3  Motivation of the Research  p.4 / Chapter 1.4  Overview of the Thesis  p.5 / Chapter 2  Related Work  p.7 / Chapter 2.1  Minconflicts Heuristic  p.7 / Chapter 2.2  GSAT  p.8 / Chapter 2.3  Breakout Method  p.8 / Chapter 2.4  GENET  p.9 / Chapter 2.5  EGENET  p.9 / Chapter 2.6  DLM  p.10 / Chapter 2.7  Simulated Annealing  p.11 / Chapter 2.8  Genetic Algorithms  p.12 / Chapter 2.9  Tabu Search  p.12 / Chapter 2.10  Integer Programming  p.13 / Chapter 3  Background  p.15 / Chapter 3.1  GENET  p.15 / Chapter 3.1.1  Network Architecture  p.15 / Chapter 3.1.2  Convergence Procedure  p.18 / Chapter 3.2  Classical Optimization  p.22 / Chapter 3.2.1  Optimization Problems  p.22 / Chapter 3.2.2  The Lagrange Multiplier Method  p.23 / Chapter 3.2.3  Saddle Point of Lagrangian Function  p.25 / Chapter 4  Binary CSP's as ZeroOne Integer Constrained Minimization Prob lems  p.27 / Chapter 4.1  From CSP to SAT  p.27 / Chapter 4.2  From SAT to ZeroOne Integer Constrained Minimization  p.29 / Chapter 5  A Continuous Lagrangian Approach for Solving Binary CSP's  p.33 / Chapter 5.1  From Integer Problems to Real Problems  p.33 / Chapter 5.2  The Lagrange Multiplier Method  p.36 / Chapter 5.3  Experiment  p.37 / Chapter 6  A Discrete Lagrangian Approach for Solving Binary CSP's  p.39 / Chapter 6.1  The Discrete Lagrange Multiplier Method  p.39 / Chapter 6.2  Parameters of CSVC  p.43 / Chapter 6.2.1  Objective Function  p.43 / Chapter 6.2.2  Discrete Gradient Operator  p.44 / Chapter 6.2.3  Integer Variables Initialization  p.45 / Chapter 6.2.4  Lagrange Multipliers Initialization  p.46 / Chapter 6.2.5  Condition for Updating Lagrange Multipliers  p.46 / Chapter 6.3  A Lagrangian Reconstruction of GENET  p.46 / Chapter 6.4  Experiments  p.52 / Chapter 6.4.1  Evaluation of LSDL(genet)  p.53 / Chapter 6.4.2  Evaluation of Various Parameters  p.55 / Chapter 6.4.3  Evaluation of LSDL(max)  p.63 / Chapter 6.5  Extension of LSDL  p.66 / Chapter 6.5.1  Arc Consistency  p.66 / Chapter 6.5.2  Lazy Arc Consistency  p.67 / Chapter 6.5.3  Experiments  p.70 / Chapter 7  Extending LSDL for General CSP's: Initial Results  p.77 / Chapter 7.1  General CSP's as Integer Constrained Minimization Problems  p.77 / Chapter 7.1.1  Formulation  p.78 / Chapter 7.1.2  Incompatibility Functions  p.79 / Chapter 7.2  The Discrete Lagrange Multiplier Method  p.84 / Chapter 7.3  A Comparison between the Binary and the General Formulation  p.85 / Chapter 7.4  Experiments  p.87 / Chapter 7.4.1  The Nqueens Problems  p.89 / Chapter 7.4.2  The Graphcoloring Problems  p.91 / Chapter 7.4.3  The CarSequencing Problems  p.92 / Chapter 7.5  Inadequacy of the Formulation  p.94 / Chapter 7.5.1  Insufficiency of the Incompatibility Functions  p.94 / Chapter 7.5.2  Dynamic Illegal Constraint  p.96 / Chapter 7.5.3  Experiments  p.97 / Chapter 8  Concluding Remarks  p.100 / Chapter 8.1  Contributions  p.100 / Chapter 8.2  Discussions  p.102 / Chapter 8.3  Future Work  p.103 / Bibliography  p.105

13 
Envelopes, duality, and multipliers for certain nonlocally convex HardyLorentz spacesLengfield, Marc. Oberlin Daniel M. January 2004 (has links)
Thesis (Ph. D.)Florida State University, 2004. / Advisor: Dr. Daniel M. Oberlin, Florida State University, College of Arts and Sciences, Dept. of Mathematics. Title and description from dissertation home page (June 18, 2004). Includes bibliographical references.

14 
Type I multiplier representations of locally compact groups / by A.K. HolzherrHolzherr, A. K. (Anton Karl) January 1982 (has links)
Includes bibliographical references / 123, [10] leaves ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Thesis (Ph.D.)University of Adelaide, Dept. of Pure Mathematics, 1984

15 
An ADMM approach to the numerical solution of state constrained optimal control problems for systems modeled by linear parabolic equationsSong, Yongcun 05 July 2018 (has links)
We address in this thesis the numerical solution of state constrained optimal control problems for systems modeled by linear parabolic equations. For the unconstrained or controlconstrained optimal control problem, the first order optimality condition can be obtained in a general way and the associated Lagrange multiplier has low regularity, such as in the L²(Ω). However, for stateconstrained optimal control problems, additional assumptions are required in general to guarantee the existence and regularity of Lagrange multipliers. The resulting optimality system leads to difficulties for both the numerical solution and the theoretical analysis. The approach discussed here combines the alternating direction of multipliers (ADMM) with a conjugate gradient (CG) algorithm, both operating in wellchosen Hilbert spaces. The ADMM approach allows the decoupling of the state constraints and the parabolic equation, in which we need solve an unconstrained parabolic optimal control problem and a projection onto the admissible set in each iteration. It has been shown that the CG method applied to the unconstrained optimal control problem modeled by linear parabolic equation is very efficient in the literature. To tackle the issue about the associated Lagrange multiplier, we prove the convergence of our proposed algorithm without assuming the existence and regularity of Lagrange multipliers. Furthermore, a worst case O(1/k) convergence rate in the ergodic sense is established. For numerical purposes, we employ the finite difference method combined with finite element method to implement the timespace discretization. After full discretization, the numerical results we obtain validate the methodology discussed in this thesis.

16 
Optimal harvesting models for metapopulations / Geoffrey N. Tuck.Tuck, Geoffrey N. (Geoffrey Neil) January 1994 (has links)
Bibliography: leaves 217238. / ix, 238 leaves ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Thesis (Ph.D.)University of Adelaide, Dept. of Applied Mathematics, 1995?

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Estimativas para entropia de operadores multiplicadores de séries de Walsh / Estimatives for entropy of multiplier operators of Walsh seriesMilaré, Gustavo Henrique 03 November 2011 (has links)
Orientador: Sergio Antonio Tozoni / Dissertação (mestrado)  Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Cientifica / Made available in DSpace on 20180818T00:43:47Z (GMT). No. of bitstreams: 1
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Previous issue date: 2011 / Resumo: As funções de Walsh formam um conjunto ortonormal completo de L2 [0; 1) que pode ser aplicado em diferentes situações tais como transmissão de dados, filtração, enriquecimento de imagem, análise de sinais e reconhecimento de padrão. Inicialmente estudamos alguns resultados básicos da Teoria dos Martingais, tais como a convergência de martingais, a Desigualdade de Doob e estimativas para a norma Lp da função quadrática associada a um martingal. Em seguida, estes resultados são usados no estudo da convergência das séries de Walsh em Lp e em um teorema de multiplicadores de séries de Walsh com a condição de Marcinkiewicz. Os resultados principais estudados nesta dissertação são estimativas de ordem de crescimento de entropia de operadores multiplicadores de séries de Walsh limitados de Lp em Lq / Abstract: The Walsh functions form a complete orthonormal set of functions of L2 [0; 1) which can be applied in different situations such as data transmission, filtering, image enhancement, signal analysis and patern recognition. Initially we study some basic results of the Theory of martingales, such as the convergence of martingales, Doob's inequality and estimatives for the Lp norm of the quadratic function associated to a martingale. Later, these results are used in the study of the convergence of the Walsh series in Lp and in a theorem of multipliers of Walsh series with Marcinkiewicz condition. The main results studied in this dissertation are estimatives of order of growth of entropy of limited multiplier operators of Walsh series from Lp to Lq / Mestrado / Analise / Mestre em Matemática

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nLarguras de conjuntos de funções suaves sobre a esfera 'S POT. d' / nWidths of sets of smooth functions on the sphere 'S POT. d'Stábile, Régis Leandro Braguim, 1985 03 May 2009 (has links)
Orientadores: Alexander Kushpel, Sergio Antonio Tozoni / Dissertação (mestrado)  Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 20180813T06:22:45Z (GMT). No. of bitstreams: 1
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Previous issue date: 2009 / Resumo: O objetivo principal da dissertação é realizar um estudo sobre estimativas de nlarguras de conjuntos de funções suaves sobre a esfera unitária ddimensional real. Esses conjuntos são gerados por operadores multiplicadores. Outro objetivo é desenvolver um texto em português sobre as nlarguras mais importantes, suas propriedades e suas relações. Este objetivo é realizado no primeiro capítulo. No segundo capítulo é realizado um estudo rápido e com poucas demonstrações sobre Análise Harmônica na esfera ddimensional real.
No terceiro capítulo são estudadas estimativas de médias de Levy para uma classe de normas especiais e em seguida esses resultados são aplicados no estudo de estimativas inferiores para as nlarguras de Kolmogorov e Gel'fand e superiores para a de Kolmogorov,
para operadores multiplicadores gerais. No quarto e último capítulo são estudadas estimativas para nlarguras de conjuntos de funções suaves, finitamente e infinitamente diferenciáveis sobre a esfera. Várias dessas estimativas são assintoticamente exatas em termos de ordem e as constantes que determinam a ordem dessas estimativas são determinadas explicitamente. / Abstract: The purpose of this work is to study estimates of nwidths of sets of smooth
functions on the ddimensional real unitary sphere. These sets are generated by multipliers
operator. Another aim is to develop a text in portuguese about the most important nwidths,
your properties and relations. We do this in the first chapter. In the second chapter, we develop a brief and proofless study about Harmonic Analysis on the ddimensional real unitary sphere. In the third chapter, the Levy means for a class of special norms are studied and applied in the study of lower estimates for the Kolmorogov and Gel'fand's nwidths, and upper estimates for the Kolmorogov's, for general multipliers operators. In the fourth and last chapter, the estimates for the nwidths of sets of smooth functions, finitely and infinitely differentiables on the sphere are studied. Several of these estimates are asymptotically exacts in terms of order and the constants that determine the order of these estimatives are given in a explicit form. / Mestrado / Mestre em Matemática

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Estimativas para nLarguras e números de entropia de conjuntos de funções suaves sobre o toro T^d / Estimates for nWidths and entropy numbers of sets of smooth functions on the torus T^dStábile, Régis Leandro Braguim, 1985 25 August 2018 (has links)
Orientador: Sergio Antonio Tozoni / Tese (doutorado)  Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica / Made available in DSpace on 20180825T19:58:00Z (GMT). No. of bitstreams: 1
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Previous issue date: 2014 / Resumo: As teorias de nlarguras e de entropia foram introduzidas por Kolmogorov na década de 1930. Desde então, muitos trabalhos têm visado obter estimativas assintóticas para nlarguras e números de entropia de diferentes classes de conjuntos. Neste trabalho, investigamos nlarguras e números de entropia de operadores multiplicadores definidos sobre o toro ddimensional. Na primeira parte, estabelecemos estimativas inferiores e superiores para nlarguras e números de entropia de operadores multiplicadores gerais. Na segunda parte, aplicamos estes resultados para operadores multiplicadores específicos, associados a conjuntos de funções finitamente e infinitamente diferenciáveis sobre o toro. Em particular, demonstramos que as estimativas obtidas são exatas em termos de ordem em diversas situações / Abstract: The theories of nwidths and entropy were introduced by Kolmogorov in the 1930s. Since then, many works aims to find estimates for nwidths and entropy numbers of different classes of sets. In this work, we investigate nwidths and entropy numbers of multiplier operators defined on the ddimensional torus. In the first part, upper and lower bounds are established for nwidths and entropy numbers of general multiplier operators. In the second part, we apply these results to specific multiplier operators, associated with sets of finitely and infinitely differentiable functions on the torus. In particular, we prove that, the estimates obtained are order sharp in various situations / Doutorado / Matematica / Doutor em Matemática

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