A smoothing Newton method for the boundary-valued ODEs

Abstract

In this thesis, we focus on the Nonsmooth Boundary-valued ODEs, whose righthandfunctions are parameterized by algebraic variables that solve the initial-valuedproblems and the nonsmooth equations. Based on the idea of the initial value techniquesused in traditional ODEs, a smoothing Newton method originated from theQSZ method is applied to the nonmsmooth dynamic systems. Most significantly,we address a reformulation of the nonsmooth ODEs to make them applicable tothe smoothing algorithm and facilitate the convergence analysis. Especially, thedifferential variational inequalities are served as the special case for discussion.