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I know that a constrained linear optimization problem can be transformed into an unconstrained binary quadratic optimization problem (UBQP). Does anyone know if the inverse result is solved in the literature? Is there a procedure to transform a UBQP problem into a constrained binary linear programming problem?

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Yes, the linearization of a product of binary variables is well known: https://or.stackexchange.com/questions/37/how-to-linearize-the-product-of-two-binary-variables

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