New quadratic lower bound for multivariate functions in global optimization

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 linear interpolant of f and a quadratic concave function. The proposed BB algorithm using this new lower bound is easy to implement and often provides high quality bounds. The performances of the proposed algorithm are compared with those of two others branch and bound algorithms, the first uses a linear lower bound and the second a quadratic lower bound. Computational results conducted on several test problems show the efficiency of the proposed algorithm.