Piecewise-linear programs are routinely used in applications to approximate nonlinear programs with a separable, concave objective function and linear constraints. We present a general and simple method for constructing and solving such problems. We use a spline algorithm to construct the approximant, a variant of the δ-form to formulate the LP, and the interior point method to solve the LP. In computational experiments on a large-scale application benchmark, the method produces a 99.7% accurate solution in a sixth of the time it takes to solve the problem exactly with a state-of-the-art nonlinear solver.