A reformulation neurodynamic algorithm for distributed nonconvex optimization

Abstract

This paper presents a reformulation neurodynamic algorithm for solving distributed nonconvex optimization problems. A class of general Lagrangian functions is introduced to eliminate the dual gap in nonconvex problems. This algorithm extends the application of neurodynamic algorithms based on the $p$-power reformulation transformation of Lagrangian functions. Under mild conditions, the initial point of the decision vector can be arbitrarily chosen. It is proven that the output trajectories will eventually converge to a strict local minimum point of the distributed nonconvex optimization problem. Finally, numerical experiments demonstrate the effectiveness of the proposed algorithm, which is also applied to solve the oblique throwing problem and the distributed source localization problem.