prior knowledge, in the form of linear inequalities that need to be satisfied over multiple polyhedral sets, is incorporated into a function approximation generated by a linear combination of linear or nonlinear kernels. in addition, the approximation needs to satisfy conventional conditions such as having given exact or inexact function values at certain points. determining such an approximation leads to a linear programming formulation. by using a nonlinear kernel and imposing the prior knowledge in the feature space rather than the input space, the nonlinear prior knowledge translates into nonlinear inequalities in the original input space. through a number of computational examples, it is shown that prior knowledge can significantly improve function approximation.