Constrained global optimization of non-polynomial problems using the Taylor-Bernstein form

In this paper, we propose a new constrained global optimization algorithm to solve non-polynomial problems. The proposed algorithm is of branch-and-bound type and use the Taylor-Bernstein form as a higher-order inclusion function for the global optimization. Several new ingredients are incorporated in the proposed algorithm to improve its efficiency, such as a improved range estimating technique along with a new simple method to generate the Taylor model of a give function. Further, different numerical experiments are conducted using the proposed algorithm on a set of 10 challenging test problems. The results of the numerical experiments are compared with the MATLAB fmincon solver and are found to be encouraging in terms of the chosen performance metrics.