A new MM algorithm for root--finding problems
- A+
：Guoliang Tian (Southern University of Science Technology)
： 2024-11-01 16:30
：Conference Room 107 at Experiment Building at Haiyun Campus
Speaker：Guoliang Tian (Southern University of Science and Technology)
Time：2024-11-1, 16:30
Location：Conference Room 107 at Experiment Building at Haiyun Campus
Abstract:
The minorization-maximization (MM) algorithm is an optimization technique to iteratively calculate the maximizer of a concave target function rather than a root-finding tool. In this paper, we in the first time develop the MM algorithm as a new method for seeking the root x* of the univariate nonlinear equation g(x)=0. The key idea is to transfer the root--finding issue to iteratively calculating the maximizer of a concave target function by designing a new MM algorithm. According to the ascent property of the MM algorithm, we know that the proposed algorithm converges to the root x* and does not depend on any initial values, in contrast to Newton's method. Some mathematical and statistical examples are provided to demonstrate the proposed algorithm.
