# Global Optimization with A Power-Transformed Objective and Gaussian Smoothing

arXiv: https://arxiv.org/abs/2412.05204 · HTML: https://mlsanity.com/paper/2412.05204/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 22 references that are in the map.
- First posted on arXiv 6 Dec 2024.

## Builds on (most cited first, 5 of 5)

- [TensorFlow: Large-Scale Machine Learning on Heterogeneous Distributed Systems](https://mlsanity.com/paper/1603.04467/) (2016)
- [ZO-AdaMM: Zeroth-Order Adaptive Momentum Method for Black-Box Optimization](https://mlsanity.com/paper/1910.06513/) (2019)
- [Single Loop Gaussian Homotopy Method for Non-convex Optimization](https://mlsanity.com/paper/2203.05717/) (2022)
- [Generalizing Gaussian Smoothing for Random Search](https://mlsanity.com/paper/2211.14721/) (2022)
- [Continuation Path Learning for Homotopy Optimization](https://mlsanity.com/paper/2307.12551/) (2023)

## Built on by (most cited first, 4 of 4)

- [Neural Predictor-Corrector: Solving Homotopy Problems with Reinforcement Learning](https://mlsanity.com/paper/2602.03086/) (2026)
- [Power Homotopy for Zeroth-Order Non-Convex Optimizations](https://mlsanity.com/paper/2511.13592/) (2025)
- [Progressive Power Homotopy for Non-convex Optimization](https://mlsanity.com/paper/2601.15915/) (2026)
- [Probabilistic Smoothing with Ratio-Monotone Transforms for Global Optimization](https://mlsanity.com/paper/2605.27316/) (2026)

## Abstract (arXiv)

We propose a novel method that solves global optimization problems in two steps: (1) perform a (exponential) power-N transformation to the not-necessarily differentiable objective function f and get fN, and (2) optimize the Gaussian-smoothed fN with stochastic approximations. Under mild conditions on f, for any δ>0, we prove that with a sufficiently large power Nδ, this method converges to a solution in the δ-neighborhood of f's global optimum point. The convergence rate is O(d2σ4varepsilon-2), which is faster than both the standard and single-loop homotopy methods if σ is pre-selected to be in (0,1). In most of the experiments performed, our method produces better solutions than other algorithms that also apply smoothing techniques.