Xiaoli Wu (Hangzhou Dianzi University, Zhejiang, China).
 
Title: Generalized Newton iteration and application of involution in polynomial optimizations

Abstract:
 
We presented a method based on symbolic-numeric reduction to geometric involutive
form to compute the primary component and a basis of Max Noether space of a
polynomial system at an isolated singular solution. The singular solution can be
known exactly or approximately. If the singular solution is known with limited
accuracy, then we proposed a generalized quadratic Newton iteration to refine it to
higher accuracy. Moreover, we applied involution criteria to polynomial optimizations.
Further consideration is to be continued.