An ordinary differential equation approach for nonlinear programming and nonlinear complementarity problem

Abstract

none

In this thesis, we consider an ordinary differential equation (ODE) approach for solving nonlinear programming (NLP) and nonlinear complementarity problem (NCP). The Karush-Kuhn Tucker (KKT) optimality conditions of NLP and NCP are used to get the new NCP-functions. A special technique is employed to reformulate of the NCP as the system of nonlinear algebraic equations (NAEs) later on reformulated once more by force of an original time-like function into an ordinary differential equation (ODE). Afterwards, a group preserving scheme (GPS) is a package to reformulate an ODE into the new numerical equation in a way the ODEs system is designed into a nonlinear dynamical system (NDS) and is continued to discover the new numerical equation through activating the Lorentz group SO 0 (n, 1) and its Lie algebra so(n, 1). Lastly, the fictitious time integration method (FTIM) is utilized into this new numerical equation to determine an approximation solution in numerical experiments area.