An inverse-free Zhang neural dynamic for time-varying convex optimization problems with equality and affine inequality constraints

Time-varying convex optimization problems have attracted a great deal of attention in many fields due to its widespread application. Particularly, the approach to time-varying convex optimization problems with equality and affine inequality constraints simultaneously is a comprehensive but complicated problem at present. In this paper, three types of inverse-free Zhang neural dynamic (ZND) including two noise-tolerance ZND models are proposed and investigated for solving time-varying convex optimization problems with equality and affine inequality constraints. It is noted that the proposed noise-tolerance ZND models own the ability to suppress noise and one of those even achieves finite-time convergency. Compared with previous work, the proposed inverse-free ZND models effectively reduce the computation complexity by simplifying the model structure and conquer the problem of solving real-time matrix inverse during the computation process, which is more appropriate for a wider practical application.