  We generalize the reduction mechanism for linear programming problems and
semidefinite programming problems from [arXiv:1410.8816] 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 SparsestCut problem, the BalancedSeparator
problem, the MaxCut problem and the Matching problem on 3-regular graphs. We
also provide a new, very strong Lasserre integrality gap result for the
IndependentSet problem, which is strictly greater than the best known LP
approximation, showing that the Lasserre hierarchy does not always provide the
tightest SDP relaxation.
