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The present paper introduces a procedure to recover an inverse parametric linear or quadratic programming problem from a given liftable polyhedral partition over which a continuous piecewise affine function is defined. The solution to the resulting parametric linear problem is exactly the initial piecewise affine function over the given original parameter space partition. We provide sufficient conditions for the existence of solutions for such inverse problems. Furthermore, the constructivedoi:10.3182/20140824-6-za-1003.02364 fatcat:r67xxob3zngdfiadlhvlury7ky