Lie群上的最速下降算法

Steepest Descent Algorithm on Lie Groups

通过对Lie群及其Lie代数的基本性质及特殊结构的分析,提出了求解一般Lie群上优化问题的最速下降算法,并对算法的收敛性作了一定的分析.得到了该算法全局收敛的两个充分条件,并在一般框架下证明了该算法至少线性收敛.通过上Riemann质心的计算问题,证明该算法可行有效.

Through analyzing special properties and structures of Lie group and its Lie algebra, a new steepest descent algorithm on Lie groups is developed. The convergence of the proposed algorithm is analyzed and achieve two sufficient conditions for the global convergence. Moreover, this paper proves that this algorithm is at least linearly convergent under the general framework. In order to show the feasibility and validity, the spacial rotation group is selected as the experimental subject.