Convex optimization

Convex optimization addresses problems where the objective function and the constraints are convex. This ensures that any local minimum is also a global minimum, providing strong guarantees of solution optimality. Its clear structure makes it widely useful in fields like machine learning, economics, and engineering, where robust and efficient identification of optimal solutions is crucial.

It is possible to frame CPU/GPU utilization as a convex optimization problem if the performance metrics and constraints can be modeled with convex functions. For instance, if the relationship between resource allocation and performance is smooth and convex (or can be approximated as such) and any decision variables can be relaxed into a convex set, then one can leverage convex optimization techniques to achieve global optimality. However, many real-world scenarios involve nonconvexities—such as discrete scheduling decisions or nonlinear performance interactions—that may require approximations or alternative optimization methods.