Optimization problem in multi-homogeneous homotopy method
Heng Liang, Xiaoyan Liu, Fengshan Bai · Optimization methods & software · 2004
Multi-homogeneous homotopy continuation method is one of the most efficient approaches in solving all isolated solutions of a polynomial system of equations. Finding the optimal partition of variables with the minimal multi-homogeneous Bézout number is clearly an optimization problem. Multi-homogeneous continuation using the optimal partition of variables reduces the computational cost in path tracking to the minimum. In this article, a heuristic method for finding the optimal variable partition is constructed based on backward greedy idea. Numerical examples show the efficiency of the method.