LP Strategy for Interval-Newton Method in Deterministic Global Optimization

A strategy is described for using linear programming (LP) to bound the solution set of the linear interval equation system that must be solved in the context of the interval-Newton method for deterministic global optimization. An implementation of this technique is described in detail, and several important issues are considered. These include selection of the interval corner required by the LP strategy and determination of rigorous bounds on the solutions of the LP problems. The impact of using a local minimizer to update the upper bound on the global minimum in this context is also considered. The procedure based on these techniques, LISS_LP, is demonstrated for several global optimization problems, with a focus on problems arising in chemical engineering. Problems with a very large number of local optima can be effectively solved, as well as problems with a relatively large number of variables.