ben-schwen
commented
1 year ago @wdkrnls AFAIK highs does not support MIQPs but only MILPs and convex QPs (see also https://github.com/ERGO-Code/HiGHS/issues/702).
For solving the best subset selection problem (for GLMs and not only linear regression) and adding additional constraints you can use the holiglm package, which lets you choose from a broad range of commercial and non-commercial solvers.
There is now a package on CRAN wrapping the open source MIP solver highs. Could this package use it so it could get on CRAN? It seems like this would be quite useful for studying variant model selection criteria following the example of the bigstep package. For example, variable selection controlling the false discovery rate following Bogdan. Maybe then something like SLOPE would have a similar relationship as with discussed in this paper compared with the MIP and what is found with bigstep using mAIC2.