Complex ZNN and GNN models for time-varying complex quadratic programming subject to equality constraints

Abstract

Zhang neural network (ZNN) has shown powerful abilities to solve a great variety of time-varying problems in the real domain. In this paper, to solve the time-varying complex quadratic programming (QP) problems in the complex domain, a new type of complex-valued ZNN is further developed and investigated. Specifically, by defining two different complex-valued error functions (termed Zhang functions), two complex ZNN models are proposed and investigated for solving the time-varying complex QP subject to complex-valued linear-equality constraints. It is theoretically proved that such two complex ZNN models globally and exponentially converge to the time-varying theoretical optimal solution of the time-varying complex QP. For comparison, the conventional gradient neural network (GNN) is developed from the real to the complex domains and then is exploited for solving the time-varying complex QP problems. Computational simulation results verify the efficacy of complex ZNN models for solving the time-varying complex QP problems. Besides, the superiorities of complex ZNN models are substantiated, as compared with complex GNN ones.