An algorithm for constrained global optimization of multivariate polynominals using the Bernstein form and John optimality conditions

We propose an algorithm for constrained global optimization of multivariate polynomials using the Bernstein form of polynomials. The proposed algorithm is of the branch and prune type, where branching is done using subdivision and pruning is done using the John optimality conditions for constrained minima. A main feature of this algorithm is that the branching and pruning operatins are done with the Bernstein polynomial coefficients. The performance of the proposed algorithm is compared with those of existing global optimization techniques, on a few examples. The obtained results show the superiority of the proposed method over existing methods, in terms of number of iterations and computational time.