Dynamic optimization by the method of generalized quasigradients

Conclusion

Since the method of generalized quasigradients is fairly general [3, 4], the results obtained with respect to the convergence of the investigated methods of dynamic optimization are applicable to a wide range of extremal problems with perhaps nondifferentiable criteria. Although the proof of the convergence was carried out for deterministic functionals as a particular case, it is easy to obtain from these results the convergence also in the case of minimization of probabilistic, dynamic functionals, when the minimum of a time-dependent regression function is sought. Such problems occur in pattern recognition, and in the development of adaptive self-organizing systems under nonstationary conditions; they can be solved by dynamic methods of stochastic approximation. By analogy with [3], the above theorems on convergence of algorithms of dynamic optimization by the method of generalized quasigradients can be used for proving the convergence in the case of minimization of dynamic problems of large dimension by the method of statistical gradients, the solution of game-type dynamic stochastic problems, etc.

In the case that it is possible to ensure a sufficiently high rate of convergence for identification of the parameters of the drift operator, it is especially convenient to use the combined method of dynamic optimization.