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Lovász and Schrijver described a generic method of tightening the LP and SDP relaxation for any 0-1 optimization problem. These tightened relaxations were the basis of several celebrated approximation algorithms (such as for MAX-CUT, MAX-3SAT, and SPARSEST CUT). We prove strong nonapproximability results in this model for well-known problems such as MAX-3SAT, Hypergraph Vertex Cover and Minimum Set Cover. We show that the relaxations produced by as many as Ω(n) rounds of the LS + procedure dodoi:10.1007/s00037-011-0027-z fatcat:fz4lo7jksrf4xphhnzt6d7zlze