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We study three methods based on linear programming and generalizations that are often applied to approximate combinatorial optimization problems. We start by describing an approximate method based on linear programming; as an example we consider scheduling of jobs on unrelated machines with costs. The second method presented is based on semidefinite programming; we show how to obtain a reasonable solution for the maximum cut problem. Finally, we analyze the conditional probabilities method in connection with randomized rounding for routing, packing and covering integer linear programming problems.