34 research outputs found
Numerical continuation methods: a perspective
AbstractIn this historical perspective the principal numerical approaches to continuation methods are outlined in the framework of the mathematical sources that contributed to their development, notably homotopy and degree theory, simplicial complexes and mappings, submanifolds defined by submersions, and singularity and foldpoint theory
Solution of nonlinear system of equations through homotopy path
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 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.Comment: arXiv admin note: text overlap with arXiv:2209.0038