We introduce a generalization of separability for global optimization, presented in the context of a simple branch and bound method. Our results apply to continuously differentiable objective functions implemented as computer programs. A significant search space reduction can be expected to...

The method investigated in this paper is concerned with the multivariate global optimization with box constraints. A new quadratic lower bound in a branch and bound framework is proposed. For a continuous, twice differentiable function f, the new lower bound is given by a difference of the...

This article presents a practicable algorithm for globally solving sum of linear ratios problem (SLR). The algorithm works by globally solving a bilinear programming problem (EQ) that is equivalent to the problem (SLR). In the algorithm, by utilizing convex envelope and concave envelope of...

Our paper considers a classic problem in the field of Truss Topology Design, the goal of which is to determine the stiffest truss, under a given load, with a bound on the total volume and discrete requirements in the cross-sectional areas of the bars. To solve this problem we propose a new...