# Primal-Dual Sequential Subspace Optimization for Saddle-point Problems

arXiv: https://arxiv.org/abs/2008.09149 · HTML: https://mlsanity.com/paper/2008.09149/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Aug 2020.

## Built on by (most cited first, 3 of 3)

- [Lifted Primal-Dual Method for Bilinearly Coupled Smooth Minimax Optimization](https://mlsanity.com/paper/2201.07427/) (2022)
- [Efficient Meta Subspace Optimization](https://mlsanity.com/paper/2110.14920/) (2021)
- [Adaptive Consensus Gradients Aggregation for Scaled Distributed Training](https://mlsanity.com/paper/2411.03742/) (2024)

## Abstract (arXiv)

We introduce a new sequential subspace optimization method for large-scale saddle-point problems. It solves iteratively a sequence of auxiliary saddle-point problems in low-dimensional subspaces, spanned by directions derived from first-order information over the primal and dual variables. Proximal regularization is further deployed to stabilize the optimization process. Experimental results demonstrate significantly better convergence relative to popular first-order methods. We analyze the influence of the subspace on the convergence of the algorithm, and assess its performance in various deterministic optimization scenarios, such as bi-linear games, ADMM-based constrained optimization and generative adversarial networks.