# Residual Expansion Algorithm: Fast and Effective Optimization for Nonconvex Least Squares Problems

## TL;DR

The Residual Expansion (RE) algorithm offers a fast, effective, and easy-to-implement method for near-global optimization in nonconvex least squares problems, outperforming traditional stochastic approaches.

## Contribution

It introduces the RE algorithm, a novel deterministic optimization technique that achieves fast, near-global solutions for nonconvex least squares problems, suitable for high-dimensional tasks.

## Key findings

- Excellent empirical performance in k-means clustering
- Effective in point-set registration and image deblurring
- Outperforms stochastic methods in speed and accuracy

## Abstract

We propose the residual expansion (RE) algorithm: a global (or near-global) optimization method for nonconvex least squares problems. Unlike most existing nonconvex optimization techniques, the RE algorithm is not based on either stochastic or multi-point searches; therefore, it can achieve fast global optimization. Moreover, the RE algorithm is easy to implement and successful in high-dimensional optimization. The RE algorithm exhibits excellent empirical performance in terms of k-means clustering, point-set registration, optimized product quantization, and blind image deblurring.