Strong reductions for extended formulations

We generalize the reduction mechanism for linear programming problems and semidefinite programming problems from Braun et al. (Inapproximability of combinatorial problems via small LPs and SDPs, 2015 ) in two ways (1) relaxing the requirement of affineness, and (2) extending to fractional optimization problems. As applications we provide several new LP-hardness and SDP-hardness results, e.g., for the problem, the problem, and the problem and show how to extend ad-hoc reductions between Sherali–Adams relaxations to reductions between LPs.