Abstract
In this paper, neural networks based on switching control approach are proposed, which is aimed at solving in real time a much wider class of nonconvex nonlinear programming problems where the objective function is assumed to satisfy only the weak condition of being regular functions. By using the gradient of the involved functions, the switching control approach proposed is shown to obey a gradient system of differential equation, and its dynamical behavior, trajectory convergence in finite time, and optimization capabilities, for nonconvex problems, are rigorously analyzed in the framework of the theory of differential equations, which are expected to enable to gain further insight on the geometrical structure of the energy landscape (objective function) of each specific class of nonlinear programming problems which is dealt with.
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