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Doctoral Thesis
DOI
10.11606/T.45.2018.tde-06012018-181441
Document
Author
Full name
John Lenon Cardoso Gardenghi
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2017
Supervisor
Committee
Birgin, Ernesto Julian Goldberg (President)
Grapiglia, Geovani Nunes
Karas, Elizabeth Wegner
Perez, José Mario Martinez
Santos, Sandra Augusta
Title in Portuguese
Complexidade em programação não linear
Keywords in Portuguese
Complexidade de avaliação
Experimentos numéricos
Otimização
Programação não linear
Abstract in Portuguese
No presente trabalho, estudamos e desenvolvemos algoritmos com análise de complexidade de avaliação de pior caso para problemas de programação não linear. Para minimização irrestrita, estabelecemos dois algoritmos semelhantes que exploram modelos de ordem superior com estratégia de regularização. Propusemos uma implementação computacional que preserva as boas propriedades teóricas de complexidade, e fizemos experimentos numéricas com problemas clássicos da literatura, a fim de atestar a implementação e avaliar a aplicabilidade de métodos que empreguem modelos de ordem superior. Para minimização com restrições, estabelecemos um algoritmo de duas fases que converge a pontos que satisfazem condições de otimalidade de primeira ordem não escaladas para o problema de programação não linear.
Title in English
Complexity in nonlinear programmin
Keywords in English
Evaluation complexity
Nonlinear programming
Numerical experiments
Optimization
Abstract in English
In the present work, we have studied and developed algorithms with worst-case evaluation complexity analysis for nonlinear programming problems. For the unconstrained optimization case, we have established two similar algorithms that explore high-order regularization models. We have proposed a computational implementation that preserves the good properties of the evaluation complexity theory, and we made numerical experiments with classical problems from the literature, in order to check the implementation and certify the practical applicability of methods that employ high-order models. For the constrained optimization case, we have established a two phases algorithm that converges to points that meet the unscaled first-order optimality condition for the nonlinear programming problem.
 
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Publishing Date
2018-02-19
 
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