Repositório Colecção: Relatórios Técnicos
https://hdl.handle.net/1822/1262
Relatórios Técnicos2024-03-28T17:04:57ZOn the degeneracy phenomenon for nonlinear optimal control problems with higher index state constraints
https://hdl.handle.net/1822/7909
Título: On the degeneracy phenomenon for nonlinear optimal control problems with higher index state constraints
Autor: Lopes, Sofia Oliveira; Fontes, Fernando A. C. C.
Resumo: Necessary conditions of optimality (NCO) play an important role in
optimization problems. They are the major tool to select a set of
candidates to minimizers. In optimal control theory, the NCO
appear in the form of a Maximum Principle (MP). For certain
optimal control problems with state constraints, it might happen
that the MP are unable to provide useful information --- the set of
all admissible solutions coincides with the set of candidates that
satisfy the MP. When this happens, the MP is said to degenerate. In
the recent years, there has been some literature on fortified forms
of the MP in such way that avoid degeneracy. These fortified forms
involve additional hypotheses --- Constraint Qualifications.
Whenever the state constraints have higher index (i.e. their first
derivative with respect to time does not depend on control), the
current constraint qualifications are not adequate. So, the main
purpose here is fortify the maximum principle for optimal control
problems with higher index constraints, for which there is a need to
develop new constraint qualifications. The results presented here are
a generalization to nonlinear problems of a previous work.
Descrição: Relatório Técnico do Núcleo de Investigação Officina Mathematica.
<b>Tipo</b>: report2008-06-04T19:11:37ZAn integral-type constraint qualification for optimal control problems with state constraints
https://hdl.handle.net/1822/6297
Título: An integral-type constraint qualification for optimal control problems with state constraints
Autor: Lopes, Sofia Oliveira; Fontes, Fernando A. C. C.; Pinho, Maria do Rosário de
Resumo: Standard necessary conditions of optimality (NCO) for constrained optimal control problems -- Maximum Principle type onditions -- may fail to provide useful information to select candidates to minimizers among the overall set of admissible solutions. This
phenomenon is known as the degeneracy phenomenon and there has been
continuing interest in the literature in proposing stronger forms of NCO that can be informative in such cases: the so-called nondegenerate NCO. The nondegenerate NCO proposed here are validunder a different set of hypothesis and under a constraint qualification of an integral-type that, in relation to some previous literature, can be verified for more problems.
Descrição: Relatório Técnico do Núcleo de Investigação Officina Mathematica.
<b>Tipo</b>: report2007-04-13T22:00:33ZFinite elements Q1-Lagrange for the linear elasticity problem
https://hdl.handle.net/1822/5198
Título: Finite elements Q1-Lagrange for the linear elasticity problem
Autor: Figueiredo, Jorge Manuel; Viaño, J. M.
Descrição: Relatório Técnico do Núcleo de Investigação Officina Mathematica.
<b>Tipo</b>: report2006-07-05T10:07:50Z