mlsanityData to 7 Oct 2026

Invex Programs: First Order Algorithms and Their Convergence

arXiv 2307.04456 ↗First posted 10 Jul 2023math.OC cs.LGcited by 1

Not on the map. Why?

Abstract (arXiv)

Invex programs are a special kind of non-convex problems which attain global minima at every stationary point. While classical first-order gradient descent methods can solve them, they converge very slowly. In this paper, we propose new first-order algorithms to solve the general class of invex problems. We identify sufficient conditions for convergence of our algorithms and provide rates of convergence. Furthermore, we go beyond unconstrained problems and provide a novel projected gradient method for constrained invex programs with convergence rate guarantees. We compare and contrast our results with existing first-order algorithms for a variety of unconstrained and constrained invex problems. To the best of our knowledge, our proposed algorithm is the first algorithm to solve constrained invex programs.

Key facts. Cited by 1 paper in the map (data through 7 Oct 2026). Builds on 14 of its 29 references that are in the map. First posted on arXiv 10 Jul 2023.

Builds on

14 of 29 references.

References · 14

  1. 2016Linear Convergence of Gradient and Proximal-Gradient Methods Under the Polyak-Lojasiewicz Conditioncited by 526
  2. 2022DAGMA: Learning DAGs via M-matrices and a Log-Determinant Acyclicity Characterizationcited by 135
  3. 2017Non-convex Optimization for Machine Learningcited by 132
  4. 2020Variational Policy Gradient Method for Reinforcement Learning with General Utilitiescited by 108
  5. 2016First-order Methods for Geodesically Convex Optimizationcited by 92
  6. 2019Near-Optimal Methods for Minimizing Star-Convex Functions and Beyondcited by 36
  7. 2017Riemannian Optimization via Frank-Wolfe Methodscited by 21
  8. 2019Simple algorithms for optimization on Riemannian manifolds with constraintscited by 14
  9. 2015Convex Learning of Multiple Tasks and their Structurecited by 13
  10. 2022Provable Acceleration of Heavy Ball beyond Quadratics for a Class of Polyak-Lojasiewicz Functions when the Non-Convexity is Averaged-Outcited by 11
  11. 2022Improved Imaging by Invex Regularizers with Global Optima Guaranteescited by 6
  12. 2021Fair Sparse Regression with Clustering: An Invex Relaxation for a Combinatorial Problemcited by 5
2 more
  1. 2022Sparse Mixed Linear Regression with Guarantees: Taming an Intractable Problem with Invex Relaxationcited by 4
  2. 2022Nonconvex Matrix Factorization is Geodesically Convex: Global Landscape Analysis for Fixed-rank Matrix Optimization From a Riemannian Perspectivecited by 3

Built on by

Cited by year

Citing papers per year: 2025: 1.

1 paper.

  1. 2025Cauchy-Schwarz Regularizerscited by 0