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EnglishTypical convergence theorems for value functions and solutions of (parametric families of) optimization problems based on È-convergence of the corresponding functionals usually rely on equi-coercivity assumptions. Without them the connection between the È-limit of the functionals and values and/or solutions of the problems may be completely broken. The question to be discussed is whether it is possible, even in the absence of a coercivity- type assumption, to ßnd limiting optimization problems (parametrized in a similar way and determined by functionals which may diÞer from the È-limits of the functionals of the sequence) such that the value functions and solutions of the problems of the sequence converge in a certain sense to those of the limiting problems. A positive answer to the question is given to a class of variational problems (containing optimal control problems with linear dynamics).
| Titolo: | On Limits of Variational Problems. The case of a Non-Coercive Functional |
| Autori: | |
| Data di pubblicazione: | 2002 |
| Rivista: | |
| Citazione: | On Limits of Variational Problems. The case of a Non-Coercive Functional / Freddi L; Ioffe A.D.. - In: JOURNAL OF CONVEX ANALYSIS. - ISSN 0944-6532. - STAMPA. - 9:2 SPEC.(2002), pp. 439-462. |
| Abstract: | Typical convergence theorems for value functions and solutions of (parametric families of) optimization problems based on È-convergence of the corresponding functionals usually rely on equi-coercivity assumptions. Without them the connection between the È-limit of the functionals and values and/or solutions of the problems may be completely broken. The question to be discussed is whether it is possible, even in the absence of a coercivity- type assumption, to ßnd limiting optimization problems (parametrized in a similar way and determined by functionals which may diÞer from the È-limits of the functionals of the sequence) such that the value functions and solutions of the problems of the sequence converge in a certain sense to those of the limiting problems. A positive answer to the question is given to a class of variational problems (containing optimal control problems with linear dynamics). |
| Handle: | http://hdl.handle.net/11390/674744 |
| Appare nelle tipologie: | 1.1 Articolo in rivista |
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http://hdl.handle.net/11390/674744
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