# Inexact Primal-Dual Gradient Projection Methods for Nonlinear Optimization on Convex Set

arXiv: https://arxiv.org/abs/1911.07758 · HTML: https://mlsanity.com/paper/1911.07758/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Nov 2019.

## Built on by (most cited first, 2 of 2)

- [Towards An Efficient Approach for the Nonconvex ℓp Ball Projection: Algorithm and Analysis](https://mlsanity.com/paper/2101.01350/) (2021)
- [An Iteratively Reweighted Method for Sparse Optimization on Nonconvex ℓp Ball](https://mlsanity.com/paper/2104.02912/) (2021)

## Abstract (arXiv)

In this paper, we propose a novel primal-dual inexact gradient projection method for nonlinear optimization problems with convex-set constraint. This method only needs inexact computation of the projections onto the convex set for each iteration, consequently reducing the computational cost for projections per iteration. This feature is attractive especially for solving problems where the projections are computationally not easy to calculate. Global convergence guarantee and O(1/k) ergodic convergence rate of the optimality residual are provided under loose assumptions. We apply our proposed strategy to l1-ball constrained problems. Numerical results exhibit that our inexact gradient projection methods for solving l1-ball constrained problems are more efficient than the exact methods.