The problems come from the SuiteSparse Matrix Collection [1].

LP: baxter, car4, ge, lp_cre_b, lp_dfl001, lp_stocfor3, rat, route, south31
Least squares: Maragal4
Power network: psse1
SVD test problem: Pd_rhs

[1] https://www.cise.ufl.edu/research/sparse/matrices/