论文标题
通过同型路径的非线性方程式解决方案
Solution of nonlinear system of equations through homotopy path
论文作者
论文摘要
该论文旨在显示非线性互补性问题与非线性方程系统之间的等效性。我们提出了一种使用向量参数$λ$的同质方法，以通过非线性方程系统找到非线性互补问题的解决方案。我们提出了一条平滑且有界的同拷贝路径，以在某些条件下获得非线性方程系统的解决方案。寡头市场的平衡问题被认为显示了拟议同型持续方法的有效性。 关键字：非线性互补性问题，非线性方程式系统，具有向量参数的同质函数，有限的平滑曲线，寡头市场平衡。
The paper aims to show the equivalency between nonlinear complementarity problem and the system of nonlinear equations. We propose a homotopy method with vector parameter $λ$ in finding the solution of nonlinear complementarity problem through a system of nonlinear equations. We propose a smooth and bounded homotopy path to obtain solution of the system of nonlinear equations under some conditions. An oligopolistic market equilibrium problem is considered to show the effectiveness of the proposed homotopy continuation method. Keywords: Nonlinear complementarity problem, system of nonlinear equations, homotopy function with vector parameter, bounded smooth curve, oligopolistic market equilibrium.
