基于Fourier 级数和半正定规划求解周期函数的e－全局最优值

One-dimensional global optimization of a function f(x) in an interval D is still a difficult problem. In this paper, we pose a new method for finding the e-global optimal value of f(x) in D . We first approximate the function f(x) via its partial sum of its Fourier series. We show that for given e, we can find a partial sum of its Fourier series such that the absolute value of their difference is less or equal than e for all x in D when n is larger than some positive number N. Then we consider finding the e -global optimal value of this partial sum, which turns out to be able to be converted into a semi-definite programming problem via some transformation, hence is able to be solved by interior point method in polynomial time.