Abstract
We present a method for solving the generalized formulation of one dimensional nonconvex variational problems. This method is based on Young measure theory, it works particularly well when the Lagrangian function has a precise polynomial structure since it uses the moments of the parametrized measures as variables. The most remarkable feature of this method is its ability to transform nonlinear nonconvex problems into convex ones. In addition, it solves a particular type of global optimization problems by estimating convex hulls of positive polynomials. We also use at some point the famous Carathéodory’s theorem.
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© 2001 Kluwer Academic Publishers
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Meziat, R., Egozcue, J.J., Pedregal, P. (2001). The Method of Moments for Nonconvex Variational Problems. In: Hadjisavvas, N., Pardalos, P.M. (eds) Advances in Convex Analysis and Global Optimization. Nonconvex Optimization and Its Applications, vol 54. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0279-7_22
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DOI: https://doi.org/10.1007/978-1-4613-0279-7_22
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-7923-6942-4
Online ISBN: 978-1-4613-0279-7
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