Global ETD Search

1	Inverse strongly monotone operators and variational inequalities Chi, Wen-te 23 June 2009 (has links) In this paper, we report existing convergence results on monotone variational inequalities where the governing monotone operators are either strongly monotone or inverse strongly monotone. We reformulate the variational inequality problem as an equivalent fixed point problem and then use fixed point iteration method to solve the original variational inequality problem. In the case of strong monotonicity case we use the Banach¡¦s contraction principle to define out iteration sequence; while in the case of inverse strong monotonicity we use the technique of averaged mappings to define our iteration sequence. In both cases we prove strong convergence for our iteration methods. An application to a minimization problem is also included. convergence iteration projection minimization Lipschitzian operator Variational inequality inverse strongly monotone averaged mapping strongly monotone monotone fixed point
2	DIRECT, analise intervalar e otimização global irrestrita / DIRECT, interval analysis and unconstrained global optimization Gonçalves, Douglas Soares, 1982- 13 August 2018 (has links) Orientador: Marcia Aparecida Gomes Ruggiero / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-08-13T09:36:27Z (GMT). No. of bitstreams: 1 Goncalves_DouglasSoares_M.pdf: 1768338 bytes, checksum: c4cc7b4b0fd9fd75e8b01510162d7662 (MD5) Previous issue date: 2009 / Resumo: Neste trabalho analisamos dois métodos para otimização global irrestrita: DIRECT, um método tipo branch-and-select, baseado em otimização Lipschitziana, com um critério especial de seleção que balanceia a ênfase entre busca local e global; e um método tipo branch-and-bound empregando as mais recentes técnicas em análise intervalar, junto com back-boxing e busca local, para acelerar o processo de convergência. Variações do método branch-and-bound intervalar, e combinaçções deste com as idéias do DIRECT foram formuladas e implementadas. A aplicação a problemas clássicos encontrados na literatura mostrou que as estratégias adotadas contribuíram para melhorar o desempenho dos algoritmos. / Abstract: In this work we analyze two unconstrained global optimization methods: DIRECT, a branch-and-select method, based on Lipschitzian optimization, with a special selection criterion that balances the emphasis between local and global search; and a branch-and-bound method incorporating the state of art interval analysis techniques, with back-boxing and local search, to speed up the convergence process. Interval branch-and-bound method variations, and combinations of them with the ideas of DIRECT were proposed and implemented. Application to classical problems found in literature, shows that the adopted strategies contribute to improve the performance of the algorithms. / Mestrado / Otimização / Mestre em Matemática Aplicada Otimização global Análise de intervalos (Matemática) Programação não-linear Otimização lipschitziana Global optimization Interval analysis (Mathematics) Nonlinear programming Lipschitzian optimization
3	On completeness of partial metric spaces, symmetric spaces and some fixed point results 10 1900 (has links) The purpose of the thesis is to study completeness of abstract spaces. In particular, we study completeness in partial metric spaces, partial metric type spaces, dislocated metric spaces, dislocated metric type spaces and symmetric spaces that are generalizations of metric spaces. It is well known that complete metric spaces have a wide range of applications. For instance, the classical Banach contraction principle is phrased in the context of complete metric spaces. Analogously, the Banach's xed point theorem and xed point results for Lipschitzian maps are discussed in this context, namely in, partial metric spaces and metric type spaces. Finally, xed point results are presented for symmetric spaces / Mathematical Sciences / Ph. D. (Mathematics) Metric space Quasi metric space Dislocated metric space Partial metric space TV S-cone metric space TV S-partial cone metric space Dislocated cone metric space Convergent sequence Cauchy sequence Convergence complete Cauchy complete 0-Cauchy complete Contraction constant Contraction map Lipschitzian constant Lipschitzian map Fixed point Metric type space Dislocated metric type space Partial metric type space Symmetric space 516.1 Metric spaces Symmetric spaces
4	On completeness of partial metric spaces, symmetric spaces and some fixed point results Aphane, Maggie 12 1900 (has links) The purpose of the thesis is to study completeness of abstract spaces. In particular, we study completeness in partial metric spaces, partial metric type spaces, dislocated metric spaces, dislocated metric type spaces and symmetric spaces that are generalizations of metric spaces. It is well known that complete metric spaces have a wide range of applications. For instance, the classical Banach contraction principle is phrased in the context of complete metric spaces. Analogously, the Banach's xed point theorem and xed point results for Lipschitzian maps are discussed in this context, namely in, partial metric spaces and metric type spaces. Finally, xed point results are presented for symmetric spaces. / Geography / Ph. D. (Mathematics) Metric space Quasi metric space Dislocated metric space Partial metric space TV S-cone metric space TV S-partial cone metric space dislocated cone metric space Convergent sequence Cauchy sequence 0-Cauchy sequence Convergence complete Cauchy complete 0-Cauchy complete Contraction constant Contraction map Lipschitzian constant Lipschitzian map Fixed point Metric type space Dislocated metric type space Partial metric type space Symmetric space 514.325 Metric spaces Symmetric spaces Fixed point theory

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