This paper develops a novel method—the global descent method—for solving a general class of global optimization problems. This method moves from one local minimizer of the objective function $f$ to a better one at each iteration with the help of an auxiliary function termed the global descent function. The global descent function is not only guaranteed to have a local minimizer $x'$ over the problem domain in $\mathbb{R}^n$ but also ensures that each of its local minimizers is located in some neighborhoods of a better minimizer of $f$ with $f(x')