The parameter continuation (homotopy) method for solving nonlinear equations and its numerical implementation are considered. An approach to the application of the continuation method for finding the Pontryagin extremals in optimal control problems is described and studied. Some techniques of expansion of this approach to control-nonlinear optimal control problems and to problems with nonsmooth control domains are proposed. The algorithms described in this paper were numerically implemented when developing the "Optimus" software package.

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