Optimal synthesis in grid schemes for quasi-convex approximation functions

A single grid algorithm which constructs the value function and the optimal synthesis, based on a local quasi-differential approximations of the Hamilton-Jacobi equation, is considered. The optimal synthesis is generated by the method of extremal translation in the direction of generalized gradients. The quasi-convex approximation functions, for which it is possible to use a linear dependence of the space-time steps for correct interpolation of the nodal optimal control values, thus substantially reducing the amount of computation, simplifying the finite-difference formulae and permitting the use of simple operators involving constructions of the method of least squares, are investigated.