Explore optimization techniques for functions with low effective dimensionality in this 28-minute conference talk by Coralia Carțiș at the Erwin Schrödinger International Institute for Mathematics and Physics. Delve into random and deterministic subspace methods for nonconvex optimization problems, focusing on functions that vary along specific important directions or components. Learn how the effective subspace of variation can be efficiently identified before the optimization process begins, and compare this approach to random embedding techniques. Examine local optimization strategies, including efficient subspace selection methods that combine randomization with expert deterministic choices. Gain insights from this presentation, which was part of the "One World Optimization Seminar in Vienna" workshop held at ESI in June 2024.