An Extended Quasilinearization Algorithm

The quasilinearization algorithm for the solution of two-point boundary-value problems is extended to handle a general class of multipoint boundary value problems involving multiple subarcs, state and/or control variable inequality constraints, and discontinuous state and/or adjoint variables. The corner and final times are unspecified since they are implicitly defined by the satisfaction of subarc stopping conditions. The inequality constraints are handled directly without the use of penalty functions. The extended algorithm is applied to a discontinuous version of the brachistochrone problem, and good convergence properties are obtained.