Algorithms for Constrained Global Optimization of Nonlinear (Polynomial) Programming Problems: The Multi Segment Polynomial B-Spline Approach

Abstract

In this paper, we propose algorithms based on polynomial B-spline form for constrained global optimization of multivariate polynomial functions. The proposed algorithms are based on a branch-and-bound framework. The performance of the proposed algorithm is tested and compared on set of test problems. We compare optimal value of global minimum obtained using the proposed algorithms with GloptiPoly and several state-of-the-art NLP solvers, on set of 11 test problems. The results of the tests show the superiority of the proposed algorithm, in that it always captures the global minimum to the user-specified accuracy.