How to quickly and stably realize the degree reduction of the rational Bezier curve is an open problem in CAGD. Based on the weighted least squares method and weighted sum method of multi-objective optimization, this paper transforms the degree reduction problem of the rational B\'ezier curve into a convex optimization problem and then uses quadratic programming to solve it. Prove that the solution is the minimum. Numerical experiments show that the method is fast and stable.

翻译：如何快速和稳步地实现理性贝塞尔曲线的降度是 CAGD 中尚未解决的问题。 根据加权最小平方法和多目标优化加权总和法,本文将理性B\'ezier曲线的降度问题转化为一个峰值优化问题,然后使用四边程序来解决这个问题。证明解决方案是最小的。数字实验显示该方法快速稳定。