Editing Linear programming (section)

==== Current matrix multiplication time algorithm ====
In 2019, Cohen, Lee and Song improved the running time to <math>\tilde O( ( n^{\omega} + n^{2.5-\alpha/2} + n^{2+1/6} ) L)</math> time, <math> \omega </math> is the exponent of [[matrix multiplication]] and <math> \alpha </math> is the dual exponent of [[matrix multiplication]].<ref>{{cite conference|title= Solving Linear Programs in the Current Matrix Multiplication Time | conference = 51st Annual ACM Symposium on the Theory of Computing  |last1=Cohen|first1=Michael B.|last2=Lee|first2=Yin-Tat|last3=Song|first3=Zhao |year=2018| arxiv =  1810.07896 | series = STOC'19 }}</ref>  <math> \alpha </math> is (roughly) defined to be the largest number such that one can multiply an <math> n \times n </math> matrix by a <math> n \times n^\alpha </math> matrix in <math> O(n^2) </math> time. In a followup work by Lee, Song and Zhang, they reproduce the same result via a different method.<ref>{{cite conference|title= Solving Empirical Risk Minimization in the Current Matrix Multiplication Time | conference = Conference on Learning Theory |last1=Lee|first1=Yin-Tat|last2=Song|first2=Zhao |last3=Zhang|first3=Qiuyi|year=2019| arxiv = 1905.04447 | series = COLT'19 }}</ref> These two algorithms remain <math>\tilde O( n^{2+1/6} L ) </math> when <math> \omega = 2 </math> and <math> \alpha = 1 </math>. The result due to Jiang, Song, Weinstein and Zhang improved <math> \tilde O ( n^{2+1/6} L) </math> to <math> \tilde O ( n^{2+1/18} L) </math>.<ref>{{cite conference|title= Faster Dynamic Matrix Inverse for Faster LPs |last1=Jiang|first1=Shunhua|last2=Song|first2=Zhao |last3=Weinstein|first3=Omri|last4=Zhang|first4=Hengjie|year=2020| arxiv = 2004.07470 }}</ref>