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Doctoral Thesis
DOI
https://doi.org/10.11606/T.45.2000.tde-20210729-122909
Document
Author
Full name
Paulo José da Silva e Silva
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2000
Supervisor
Title in Portuguese
Tópicos em métodos de ponto proximal
Keywords in Portuguese
Análise Numérica
Desigualdades Variacionais
Otimização Convexa
Teoria De Sistemas E Controle
Abstract in Portuguese
Este trabalho insere-se no contexto de métodos de ponto proximal para a resolução de problemas de desigualdade variacional e otimização convexa e sua conexão com métodos de multiplicadores. Apresentamos duas novas classes de regularização e os respectivos métodos proximais. A primeira, bastante simples, baseia-se em translações de funções estritamente convexas. A segunda consiste de uma ampla gama de regularizações coercivas que estende resultados recentes da literatura. Em particular, estendemos as idéias de Auslender et al. sobre regularizações duplas de forma a conterem distâncias de Bregman, com operadores que não são, necessariamente, para-monótonos. Analisamos também a ligação destes métodos com os respectivos métodos de multiplicadores. Por fim, apresentamos novos critérios para aceitação de soluções aproximadas dos sub-problemas que devem ser resolvidos pelos métodos de multiplicadores
Title in English
not available
Abstract in English
This thesis deals with proximal point methods and their use to solve variational inequalities and convex optimization problems. We present two new regularizations families and the respective proximal methods. The first family, simple in concept, is based on translations of sctrict convex functions. The second family contains a broad class of coercive regularizations, extending recent results in the literature. In particular, we extended the double regularizations presented by Auslenderet al. to a wide class that contains Bregman distances and we succeed to prove that these regularizations may be used to solve variational inequalities with maximal monotone operators that may not be para-monotone. We also explore the relationship of proximal and multiplier methods. Finally, we present some new criteria to accept approximate solutions of the unconstrained problems that have to be solved by multiplier methods
 
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Publishing Date
2021-07-29
 
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