# Gradient projection and conditional gradient methods for constrained nonconvex minimization

arXiv: https://arxiv.org/abs/1906.11580 · HTML: https://mlsanity.com/paper/1906.11580/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Jun 2019.

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

- [Fast and accurate optimization on the orthogonal manifold without retraction](https://mlsanity.com/paper/2102.07432/) (2021)
- [Gradient-free optimization of highly smooth functions: improved analysis and a new algorithm](https://mlsanity.com/paper/2306.02159/) (2023)
- [Intruding with Words: Towards Understanding Graph Injection Attacks at the Text Level](https://mlsanity.com/paper/2405.16405/) (2024)
- [Policy Gradient for Continuous-Time Robust Markov Decision Processes](https://mlsanity.com/paper/2606.04335/) (2026)

## Abstract (arXiv)

Minimization of a smooth function on a sphere or, more generally, on a smooth manifold, is the simplest non-convex optimization problem. It has a lot of applications. Our goal is to propose a version of the gradient projection algorithm for its solution and to obtain results that guarantee convergence of the algorithm under some minimal natural assumptions. We use the Lezanski-Polyak-Lojasiewicz condition on a manifold to prove the global linear convergence of the algorithm. Another method well fitted for the problem is the conditional gradient (Frank-Wolfe) algorithm. We examine some conditions which guarantee global convergence of full-step version of the method with linear rate.