The parameterization method in singular differential-algebraic equations

Abstract

The paper is devoted to the circumstantiation of the parameterization method for classical calculus of variation problems corresponding to the non-linear ODEs. The method is based on a finite parameterization of "control" functions (finitely entering in initial system) and on derivation of the problem functional with respect to control parameters. The first and the second derivatives are calculated with the help of adjoint vector and matrix impulses. The problems of arising degeneration of gradients and optimality conditions of the first order are overcome by using the Newton method. Results of the solution to degenerate DAEs, particularly with non-unique solutions, are presented. © Springer-Verlag Berlin Heidelberg 2003.