On new methods to construct lower bounds in simplicial branch and bound based on interval arithmetic

Abstract Branch and Bound (B&B) algorithms in Global Optimization are used to perform an exhaustive search over the feasible area. One choice is use simplicial partition sets. Obtaining sharp cheap bounds of objective function a simplex very important construction efficient B&B algorithms. Although enclosing box implies overestimation, boxes more natural when dealing with individual coordinate bounds, bounding ranges Interval Arithmetic (IA) computationally cheap. This paper introduces several linear relaxations using gradient information Affine experimentally studies their efficiency compared traditional lower obtained by centered IA forms adaption simplices. A algorithm monotonicity test compare set low dimensional problems instances that either have constrained region or where simplex. Numerical results show it possible obtain tight subsets.