A Survey of Neurodynamic Approach for Nonconvex Optimization Problems

With the development of computer science and artificial intelligence, the nonconvexity has emerged as an indispensable property for many practical problems. Inspired by the applications involving machine learning, sensor networks and cloud computing, a variety of nonconvex optimization models have been developed. The nonconvex models mainly include nonconvex cost functions and nonconvex constraints. Also, the nonconvex constraints including nonconvex equality constraint, nonconvex inequality constraint, etc. Compared with convex optimization problems, solving a nonconvex optimization problem is in general NP-hard. Many algorithms cannot directly meet the optimization problems with nonconvex objective functions or nonconvex constraints. As an efficient parallel-processing method, the neurodynamic approaches usually exhibit high robustness and fast convergence near the local minima of the nonconvex problems. As such, neurodynamic approaches are now considered powerful nonconvex optimization tools with widespread applications. Moreover, the combination of neurodynamic approaches with many heuristic algorithms showcases enormous global solving ability to nonconvex optimization problems. Thus, this paper is designed to provide a comprehensive overview of existing neurodynamic approach for nonconvex optimization problems.