Nonlinear duality and multiplier theorems
The main purpose of this paper is to extend the John theorem on nonlinear programming with inequality contraints and the Mangasarian-Fromovitz theorem on nonlinear programming with mixed constraints to any real normed linear space. In addition, for the John theorem assuming Frechet differentiability...
- Autores:
-
Azpeitia, Alfonso G.
- Tipo de recurso:
- Article of journal
- Fecha de publicación:
- 1987
- Institución:
- Universidad Nacional de Colombia
- Repositorio:
- Universidad Nacional de Colombia
- Idioma:
- spa
- OAI Identifier:
- oai:repositorio.unal.edu.co:unal/42888
- Acceso en línea:
- https://repositorio.unal.edu.co/handle/unal/42888
http://bdigital.unal.edu.co/32986/
- Palabra clave:
- John theorem
nonlinear programming
theorem Mangasarian-Fromovitz
restrictions mixed
linear space
finite dimensional
- Rights
- openAccess
- License
- Atribución-NoComercial 4.0 Internacional
| Summary: | The main purpose of this paper is to extend the John theorem on nonlinear programming with inequality contraints and the Mangasarian-Fromovitz theorem on nonlinear programming with mixed constraints to any real normed linear space. In addition, for the John theorem assuming Frechet differentiability, the standard conclusion that the multiplier vector is not zero is sharpened to the nonvanishing of the subvector of those components corresponding to the constraints which are not linear affine. The only tools used are generalizations of the duality theorem of linear programming, and hence of the Farkas lemma, to the case of a primal real linear space of any dimension with no topological restrictions. It is shown that these generalizations are direct consequence of the ordiry duality theorem of linear programming in finite dimension. |
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