# Benign Nonconvex Landscapes in Optimal and Robust Control, Part II: Extended Convex Lifting

arXiv: https://arxiv.org/abs/2406.04001 · HTML: https://mlsanity.com/paper/2406.04001/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Jun 2024.

## Built on by (most cited first, 1 of 1)

- [Gradient Dominance in the Linear Quadratic Regulator: A Unified Analysis for Continuous-Time and Discrete-Time Systems](https://mlsanity.com/paper/2602.22577/) (2026)

## Abstract (arXiv)

Many optimal and robust control problems are nonconvex and potentially nonsmooth in their policy optimization forms. In Part II of this paper, we introduce a new and unified Extended Convex Lifting (ECL) framework to reveal hidden convexity in classical optimal and robust control problems from a modern optimization perspective. Our ECL offers a bridge between nonconvex policy optimization and convex reformulations, enabling convex analysis for nonconvex problems. Despite non-convexity and non-smoothness, the existence of an ECL not only reveals that minimizing the original function is equivalent to a convex problem but also certifies a class of first-order non-degenerate stationary points to be globally optimal. Therefore, no spurious stationarity exists in the set of non-degenerate policies. This ECL framework can cover many benchmark control problems, including state feedback linear quadratic regulator (LQR), dynamic output feedback linear quadratic Gaussian (LQG) control, and H_∞ robust control. ECL can also handle a class of distributed control problems when the notion of quadratic invariance (QI) holds. We further show that all static stabilizing policies are non-degenerate for state feedback LQR and H_∞ control under standard assumptions. We believe that the new ECL framework may be of independent interest for analyzing nonconvex problems beyond control.