Abstract:

This paper presents a global optimization algorithm for solving the general polynomial programming with box constraint. The algorithm includes two phases. In the first phase, a local optimal solution is found by a local optimization algorithm. In the second phase, with a density vector sequence on the unit ball, we transform the multivariate polynomial into univariate polynomial, and find a point which is smaller than the current local optimal point by solving the roots of univariate polynomial. We use it as the new initial point, and return to the first phase. Therefore we can get a better local optimal solution. Through repeating the two phases, we can find the global optimal solution of the problem eventually. And the convergence of the algorithm is analyzed. Finally, the numerical results show that the algorithm is effective.

Key words: general polynomial, vector sequence, global optimization, convergence