New duality results for evenly convex optimization problems

We present new results on optimization problems where the involved functions are evenly convex. By means of a generalized conjugation scheme and the perturbation theory introduced by Rockafellar, we propose an alternative dual problem for a general optimization one defined on a separated locally con...

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Detalles Bibliográficos
Autores: Fajardo Gómez, Maria Dolores, Grad, Sorin-Mihai, Vidal Núñez, José|||0000-0002-1190-6700
Tipo de recurso: artículo
Fecha de publicación:2020
País:España
Institución:Universidad de Alcalá (UAH)
Repositorio:e_Buah Biblioteca Digital Universidad de Alcalá
Idioma:inglés
OAI Identifier:oai:ebuah.uah.es:10017/68302
Acceso en línea:http://hdl.handle.net/10017/68302
https://dx.doi.org/10.1080/02331934.2020.1756287
Access Level:acceso abierto
Palabra clave:Evenly convex function
Generalized convex conjugation
Converse duality
Total duality
Lagrangian function
Convex optimization in locally convex spaces
Matermáticas
Mathematics
Descripción
Sumario:We present new results on optimization problems where the involved functions are evenly convex. By means of a generalized conjugation scheme and the perturbation theory introduced by Rockafellar, we propose an alternative dual problem for a general optimization one defined on a separated locally convex topological space. Sufficient conditions for converse and total duality involving the even convexity of the perturbation function and c-subdifferentials are given. Formulae for the c-subdifferential and biconjugate of the objective function of a general optimization problem are provided, too. We also characterize the total duality by means of the saddle-point theory for a notion of Lagrangian adapted to the considered framework.