We consider an ordinary differential equation (ODE) approach for solving non- linear programming (NLP) and nonlinear complementary problem (NCP). The Karush- Kuhn Tucker (KKT) optimality conditions can be converted to NCP. Based on the Fischer-Burmeister (FB) function and the Natural-Residual (NR) function are obtained 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 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 a discovery the new numerical equation through activating the Lorentz group SO0(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 at the numerical experiments area.
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.
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