Minimization of a multivariate function where each variable shows sinusoidal dependence with offset

Question

I'm working on minimizing a multivariate function $f(x_1, x_2, ..., x_n)$ and would appreciate some help. The function $f$ has the following properties:

1. The function's range is bounded: $0 \leq f \leq 1$. In certain cases, I know that the function can reach its minimum value of exactly $0$.
2. If we fix all variables except one, say $x_i$, and treat $f$ as a function of that single variable $g(x_i)$, $g$ takes the form: $$ f(x)\big|_{\substack{x_j=\text{const.}\\j\neq i}} =g(x_i)=A\sin⁡(x_i+\alpha)+B.$$ Here, $A, B$, and $\alpha$ are constants that depend on the fixed variables. Additionally, it's given that $A \neq 0$ and $B \neq 0$. In other words, each variable shows sinusoidal dependence with an offset.

Given the constraints and properties of the function, what would be the best approach to minimize this function? Does knowing that the minimum can be $0$ provide any additional leverage for optimization?

I've attempted to minimize this function using the L-BFGS algorithm, which led me to local minima. However, I'm interested in finding the global minimum.

Any insights, references, or suggestions would be greatly appreciated. Thanks in advance.