A recursively feasible and convergent Sequential Convex Programming procedure to solve non-convex problems with linear equality constraints [article]

Josep Virgili-Llop, Marcello Romano
2018 arXiv   pre-print
A computationally efficient method to solve non-convex programming problems with linear equality constraints is presented. The proposed method is based on a recursively feasible and descending sequential convex programming procedure proven to converge to a locally optimal solution. Assuming that the first convex problem in the sequence is feasible, these properties are obtained by convexifying the non-convex cost and inequality constraints with inner-convex approximations. Additionally, a
more » ... ationally efficient method is introduced to obtain inner-convex approximations based on Taylor series expansions. These Taylor-based inner-convex approximations provide the overall algorithm with a quadratic rate of convergence. The proposed method is capable of solving problems of practical interest in real-time. This is illustrated with a numerical simulation of an aerial vehicle trajectory optimization problem on commercial-of-the-shelf embedded computers.
arXiv:1810.10439v1 fatcat:buyftc5sxvd33j2ac2rdfugtaa