Two-Segment Separable Programming

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 not require the cumbersome "fine grid" approximations employed to achieve high accuracy in the usual separable programming approach. In addition, the new methods yield feasible solutions with objective values guaranteed to be within any specified tolerance of optimality. In computational tests with real-world problems of up to 500 "nonlinear" variables the approach has exhibited rapid convergence and yielded very close bounds on the optimal value.