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On the relation between inward pointing velocity conditions
Lopes, Sofia Oliveira; Fontes, Fernando A. C. C.; Pinho, Maria do Rosário deInward pointing velocity conditions are important in the study of whether trajectories remain within sets (the so-called invariance or viability) and also to establish constraint qualifications (CQ) under which necessary conditions of optimality for control problem can be guaranteed to be nondegenerate NCO or normal. In our research on nondegenerate NCO we have studied different types of CQs in the form of inwa...
Nondegenerate forms of the maximum principle for optimal control problems with ...
Lopes, Sofia OliveiraTese de Doutoramento em Ciências - Área de Conhecimento Matemática ; The Maximum Principle (MP) plays an important role in the characterization of solutions to optimal control problems. It typically identifies a small set of candidates where the minimizers belong. However, for some optimal control problems with constraints, it may happen that the MP is unable to provide any useful information; for example, if ...
On the degeneracy phenomenon for nonlinear optimal control problems with higher...
Lopes, Sofia Oliveira; Fontes, Fernando A. C. C.Relatório Técnico do Núcleo de Investigação Officina Mathematica. ; 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...
An integral-type constraint qualification for optimal control problems with sta...
Lopes, Sofia Oliveira; Fontes, Fernando A. C. C.; Pinho, Maria do Rosário deRelatório Técnico do Núcleo de Investigação Officina Mathematica. ; 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 ...
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