Global optimization of separable objective functions on convex polyhedra via piecewise-linear approximation

The problem of minimizing a separable nonlinear objective function under linear constraints is considered in this paper. A systematic approach is proposed to obtain an approximately globally optimal solution via piecewise-linear approximation. By means of the new approach a minimum point of the original problem confined in a region where more than one linear piece is needed for satisfactory approximation can be found by solving only one linear programming problem. Hence, the number of linear programming problems to be solved for finding the approximately globally optimal solution may be much less than that of the regions partitioned. In addition, zero-one variables are not introduced in this approach. These features are desirable for efficient computation. The practicability of the approach is demonstrated by an example.