New iterative separable programming techniques based on two-segment, piecewise-linear approximations are described for the minimization of convex separable functions over convex sets. These techniques have two advantages over traditional separable programming methods. The first is that they do...

Lowe and Hurter introduced the "generalized market area problem" of simultaneously determining production levels and distribution patterns at n plants to satisfy demand distributed over a subset of R^k. Here we give simpler proofs and extensions of their results. We also show how the problem can...