tag:blogger.com,1999:blog-593563533834706486.post8733348478467418528..comments2024-03-28T10:35:10.453-04:00Comments on Yet Another Math Programming Consultant: Median, quantiles and quantile regression as linear programming problemsErwin Kalvelagenhttp://www.blogger.com/profile/09496091402502236997noreply@blogger.comBlogger4125tag:blogger.com,1999:blog-593563533834706486.post-50086810047334120452021-07-01T05:37:24.230-04:002021-07-01T05:37:24.230-04:00Thanks. Indeed, the standard solvers I have access...Thanks. Indeed, the standard solvers I have access to are all gradient based. I could not find off-the-shelf subgradient solvers (I assume users develop them for their problem at hand).Erwin Kalvelagenhttps://www.blogger.com/profile/09496091402502236997noreply@blogger.comtag:blogger.com,1999:blog-593563533834706486.post-8800975687261355822021-06-25T16:01:19.778-04:002021-06-25T16:01:19.778-04:00The NLP model for finding the median is not differ...The NLP model for finding the median is not differentiable, that is of course correct. But it is convex in m and it has a subgradient defined at every point. A subgradient solver will reliably find the global minimum for that function.Petterhttps://www.blogger.com/profile/10458441676290777808noreply@blogger.comtag:blogger.com,1999:blog-593563533834706486.post-15017278606132330512021-06-13T05:59:06.517-04:002021-06-13T05:59:06.517-04:00In most cases it does not really matter which form...In most cases it does not really matter which formulation you choose. Here we use the variable splitting approach so we can put different weights on the positive and negative deviation in the subsequent models. Erwin Kalvelagenhttps://www.blogger.com/profile/09496091402502236997noreply@blogger.comtag:blogger.com,1999:blog-593563533834706486.post-75120794459880705612021-06-13T05:12:05.225-04:002021-06-13T05:12:05.225-04:00I did something very similar to "LP model 1 f...I did something very similar to "LP model 1 for finding the median" in my bachelor's thesis. I don't think I realized that you could also formulate it by splitting variables.Anonymoushttps://www.blogger.com/profile/00815163512534314494noreply@blogger.com