Nonconvex and Bound Constraint Zeroing Neural Network for Solving Time-Varying Complex-Valued Quadratic Programming Problem

Many methods are known to solve the problem of real-valued and static quadratic programming (QP) effectively. However, few of them are still useful to solve the time-varying QP problem in the complex domain. In this study, a nonconvex and bound constraint zeroing neural network (NCZNN) model is designed and theorized to solve the time-varying complex-valued QP with linear equation constraint. Besides, we construct several new types of nonconvex and bound constraint complex-valued activation functions by extending real-valued activation functions to the complex domain. Subsequently, corresponding simulation experiments are conducted, and the simulation results verify the effectiveness and robustness of the proposed NCZNN model. Moreover, the model proposed in this article is further applied to solve the issue of small target detection in remote sensing images, which is modeled to QP problem with linear equation constraint by a serial of conversions based on constrained energy minimization algorithm.