  Many resource allocation tasks are challenging global (i.e., non-convex)
optimization problems. The main issue is that the computational complexity of
these problems grows exponentially in the number of variables instead of
polynomially as for many convex optimization problems. However, often the
non-convexity stems only from a subset of variables. Conventional global
optimization frameworks like monotonic optimization or DC programming treat all
variables as global variables and require complicated, problem specific
decomposition approaches to exploit the convexity in some variables. To
overcome this challenge, we develop an easy-to-use algorithm that inherently
differentiates between convex and non-convex variables, preserving the low
computational complexity in the number of convex variables. Another issue with
these widely used frameworks is that they may suffer from severe numerical
problems. We discuss this issue in detail and provide a clear motivating
example. The solution to this problem is to replace the traditional approach of
finding an {\epsilon}-approximate solution by the novel concept of
{\epsilon}-essential feasibility. The underlying algorithmic approach is called
successive incumbent transcending (SIT) algorithm and builds the foundation of
our developed algorithm. A further highlight of this algorithm is that it
inherently treats fractional objectives making the use of Dinkelbach's
iterative algorithm obsolete. Numerical experiments show a speed-up of four
orders of magnitude over state-of-the-art algorithms and almost three orders of
magnitude of additional speed-up over Dinkelbach's algorithm for fractional
programs.
