A Convergence of ODE Method in Constrained Optimization

Abstract

This paper proposes a convergence theory of the ordinary differential equations (ODE) method for finding the local optima of general constrained optimization. We prove that solutions starting from the neighbourhood of a critical point of the differential equations in this paper about part variables always converge to the feasible point of the problem. We also study the initial relationship between neural computation in optimization (NCO) and ODE methods. Some detailed connections of the two methods in solving the linear and quadratic programming onRn+are shown in this paper. © 1998 Academic Press.