An ellipsoidal branch and bound algorithm for global optimization

TL;DR

This paper introduces an ellipsoidal branch and bound algorithm for global optimization, utilizing ellipsoid subdivision and affine underestimates to efficiently find global solutions.

Contribution

It presents a novel branch and bound method that employs ellipsoidal subdivisions and a ball approximation algorithm for convex relaxations, enhancing global optimization techniques.

Findings

Ball approximation algorithm performs well compared to SEDUMI and gradient projection.

The method effectively handles quadratic objectives with ellipsoidal constraints.

Experimental results demonstrate the algorithm's efficiency in global optimization tasks.

Abstract

A branch and bound algorithm is developed for global optimization. Branching in the algorithm is accomplished by subdividing the feasible set using ellipses. Lower bounds are obtained by replacing the concave part of the objective function by an affine underestimate. A ball approximation algorithm, obtained by generalizing of a scheme of Lin and Han, is used to solve the convex relaxation of the original problem. The ball approximation algorithm is compared to SEDUMI as well as to gradient projection algorithms using randomly generated test problems with a quadratic objective and ellipsoidal constraints.