Numerical comparisons based on new NCP-functions

Abstract

Abstract We consider studying numerical comparisons based on variants of new NCP-functions denoted by ϕ k p . The nonlinear programming (NLP) can be converted to nonlinear complementarity problem (NCP) by employing the Karush-Kuhn Tucker (KKT) optimality conditions. One of the most popular ways to solve NCP is Lagrangian globalization (LG) method by transforming NCP as a system of nonsmooth (semismooth) equations. The second one is a novel method named the fictitious time integration method (FTIM). We reformulate NCP as a system of nonlinear algebraic equations (NAEs) and then construct an ordinary differential equation (ODE) by utilizing time-like functions. A group preserving scheme (GPS) is a set of ODEs which is a tool for systematically reformulating into the nonlinear dynamical system (NDS). Afterward, the NDS can be manipulated to numerical equations through activating the Lorentz group SO 0(n, 1) and its Lie algebra SO 0(n, 1). The FTIM will be operated on this numerical equation in numerical simulations for getting approximation solutions. All of the numerical experiments are carried out in performance profile theories. The comparisons of new NCP-functions by utilizing FTIM and LG method will be discussed in numerical experiments. Lastly, an accurate test of both FTIM and LG method is going to be committed by performance profile concepts as well.