A recursively feasible and convergent Sequential Convex Programming procedure to solve non-convex problems with linear equality constraints
Abstract
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 computationally 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.
Cite
@article{arxiv.1810.10439,
title = {A recursively feasible and convergent Sequential Convex Programming procedure to solve non-convex problems with linear equality constraints},
author = {Josep Virgili-Llop and Marcello Romano},
journal= {arXiv preprint arXiv:1810.10439},
year = {2018}
}