USE OF THE METHOD OF DIFFERENTIAL DESCENTS FOR THE SOLUTION OF NONLINEAR SYSTEMS,
FOREIGN TECHNOLOGY DIV WRIGHT-PATTERSON AFB OHIO
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The authors prove local theorems concerning the stabilization of the trajectories of the differential descent towards the points of the minimum of the function and to the solutions of the nonlinear systems. Basic functional identities and inequalities are derived. The local theorems are then applied to an investigation of the stabilization of trajectories towards the solution in the case when the solution is a simple nondegenerate root. This is followed by a study of the behavior of the trajectories in the vicinity of a rigorously nondegenerate manifold of solutions. The theory of the differential descent is then developed for direct application in the complex form. The article completes with a study of the differential descent as a whole, with the problem considered in general form on Riemann manifolds. The main result is that for almost all initial points, the trajectory of the differential descent stabilizes towards a solution of the nonlinear system or towards the point of minimum of the function.
- Theoretical Mathematics