From a Nonlinear, Nonconvex Variational Problem to a Linear, Convex Formulation |
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| Authors: | José Egozcue Meziat Pedregal |
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| Affiliation: | (1) ETS d'Enginyers de Camins, Canals i Ports, Gran Capità, s/n, 08034 Barcelona, Spain juanjose.egozcue@upc.es , ES;(2) ETI Telecomunicaciones, Universidad de Castilla-La Mancha, 16071 Cuenca, Spain and Departamento de Matemáticas, Universidad de los Andes, Carrera 1, N 18A-10 Bogotá, Colombia rmeziat@uniandes.edu.co , CO;(3) ETSI Industriales, Universidad de Castilla-La Mancha, 13071 Ciudad Real, Spain pablo.pedregal@uclm.es, ES |
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| Abstract: | Abstract. We propose a general approach to deal with nonlinear, nonconvex variational problems based on a reformulation of the problem resulting in an optimization problem with linear cost functional and convex constraints. As a first step we explicitly explore these ideas to some one-dimensional variational problems and obtain specific conclusions of an analytical and numerical nature. |
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| Keywords: | . Convexification Young measures Moments. AMS Classification. 49J05 49J45 49M37. |
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