A neurodynamic optimization approach to nonconvex resource allocation problem

A neurodynamic optimization approach characterized by a negative subgradient flow (NSF) is proposed to solve distributed nonconvex resource allocation problem (DNRAP). Under some mild assumptions, it is proved that the state solutions of the proposed approach converge to the critical point set of the considered DNRAP. Moreover, benefiting from the well-known nonsmooth Lojasiewicz inequality, analysis results show that the state solutions converge toward a critical point (not set) of the considered DNRAP. The convergence rate of the state solution, including exponential or finite-time convergence, can be evaluated through the quantitative calculation of Lojasiewicz exponent. Furthermore, we assess the related Lojasiewicz exponent of presented NSF in some special situation, for instance, in nonconvex quadratic programming. Finally, simulation illustrates the well performance of presented neurodynamic optimization approach.