Acceleration of αBB algorithm using quadratic underestimator in global optimization

Abstract

Many global optimization techniques employ the branch-and-bound algorithm as their framework of refining search regions. So called αBB is one such example which utilizes twice-differentiable convex underestimator during the branch-and-bound procedure. The underestimator of αBB may be too conservative with the increase of the degree of complexity of functions. In this research, a new underestimator is presented to make tight underestimator and accelerate convergence of αBB global optimization iteration procedure. The new tight underestimator has quadratic form which has the minimum points at the center of search regions. A new quadratic underestimator is derived and the technique to generate the quadratic underestimator is described. The branch-and-bound algorithm is used as the framework. And the quadratic underestimator is applied to solve the unconstrained global optimization. The number of iterations and overall computational time are obtained with the quadratic underestimator and the underestimator of αBB. The results with the quadratic underestimator are compared with the underestimator of αBB. Relative computational time is addressed. From the final result, the new tight underestimator exhibits better convergence for higher dimensional problems.