On Monotonicity Detection in Simplicial Branch and Bound over a Simplex

Abstract

Abstract The concept of exploiting proven monotonicity for dimension reduction and elimination of partition sets is well known in the field of Interval Arithmetic Branch and Bound (B &B). Part of the concepts can be applied in simplicial B &B over a box. The focus of our research is here on minimizing a function over a lower simplicial dimension feasible set, like in blending and portfolio optimization problems. How can monotonicity be detected and be exploited in a B &B context? We found that feasible directions can be used to derive bounds on the directional derivative. Specifically, Linear Programming can be used to detect the sharpest bounds.