In this paper we present an approach to determine the local minima of a specific class of minimization problems. Attention is focused on the inextensibility condition of flexible rods expressed as a non convex constraint. Two algorithms are derived from a special splitting of the Lagrangian into the difference of two convex functions (DC). They are compared to the classical augmented Lagrangian method used in this context. These DC formulations are easily extended to contact problems and applied to the determination of confined postbuckling shapes and to microbuckling in a cellular structure.