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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José Egozcue, ., Meziat, . & Pedregal, . From a Nonlinear, Nonconvex Variational Problem to a Linear, Convex Formulation . Appl Math Optim 47, 27–44 (2002). https://doi.org/10.1007/s00245-002-0738-2
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DOI: https://doi.org/10.1007/s00245-002-0738-2