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Modification of gradient type methods in optimal control problems. (English. Russian original) Zbl 1063.49023
Russ. Math. 46, No. 12, 64-76 (2002); translation from Izv. Vyssh. Uchebn. Zaved. Mat. 2002, No. 12, 66-78 (2002).
The paper is a continuation of the previous paper by V. A. Srochko and N. V. Mamonova [Russ. Math. 45, No. 12, 52–64 (2001); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2001, No. 12, 55–67 (2001; Zbl 1057.49022)] and is devoted to modifications of the Frank-Wolfe (conditional gradient) method applied to the general smooth optimal control problem. The author considers the task of optimal choice of the variation function with respect to some classes of parameters and norms. Such mixed type approximations are proposed to be used in conditional gradient methods.

49M37 Numerical methods based on nonlinear programming
49M05 Numerical methods based on necessary conditions
49N10 Linear-quadratic optimal control problems