Mirror Descent-Type Algorithms for the Variational Inequality Problem with Functional Constraints
Mirrored from arXiv — Machine Learning for archival readability. Support the source by reading on the original site.
Computer Science > Machine Learning
arXiv:2605.16262 (cs)
[Submitted on 24 Feb 2026]
Title:Mirror Descent-Type Algorithms for the Variational Inequality Problem with Functional Constraints
View a PDF of the paper titled Mirror Descent-Type Algorithms for the Variational Inequality Problem with Functional Constraints, by Mohammad S. Alkousa and 3 other authors
View PDF
HTML (experimental)
Abstract:Variational inequalities play a key role in machine learning research, such as generative adversarial networks, reinforcement learning, adversarial training, and generative models. This paper is devoted to the constrained variational inequality problems with functional constraints (inequality-type constraints). We propose some mirror descent-type algorithms that switch between productive and non-productive steps depending on the values of the functional constraints at iterations, with many different step size rules and stopping criteria. We analyze the proposed algorithms and prove their optimal convergence rate to achieve a solution with desired accuracy, for problems with bounded and monotone operators and Lipschitz convex functional constraints. In addition, we propose a modification of the proposed algorithms by considering each functional constraint in the calculation when we have a productive step, as well as the first constraint that violates the feasibility. This modification can save the running time of algorithms when we have many functional constraints. In addition, we provide an analysis of the proposed algorithms for $\delta$-monotone operators, allowing us to apply the proposed algorithms, as a special case, to constrained minimization problems when we do not have access to the exact information about the subgradient of the objective function. Numerical experiments that illustrate the work and performance of the proposed algorithms are also given.
| Subjects: | Machine Learning (cs.LG); Optimization and Control (math.OC) |
| Cite as: | arXiv:2605.16262 [cs.LG] |
| (or arXiv:2605.16262v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2605.16262
arXiv-issued DOI via DataCite
|
Full-text links:
Access Paper:
- View PDF
- HTML (experimental)
- TeX Source
View a PDF of the paper titled Mirror Descent-Type Algorithms for the Variational Inequality Problem with Functional Constraints, by Mohammad S. Alkousa and 3 other authors
Current browse context:
cs.LG
References & Citations
Loading...
Bookmark
Bibliographic Tools
Code, Data, Media
Demos
Related Papers
About arXivLabs
Bibliographic and Citation Tools
Bibliographic Explorer Toggle
Bibliographic Explorer (What is the Explorer?)
Connected Papers Toggle
Connected Papers (What is Connected Papers?)
Litmaps Toggle
Litmaps (What is Litmaps?)
scite.ai Toggle
scite Smart Citations (What are Smart Citations?)
Code, Data and Media Associated with this Article
alphaXiv Toggle
alphaXiv (What is alphaXiv?)
Links to Code Toggle
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
DagsHub Toggle
DagsHub (What is DagsHub?)
GotitPub Toggle
Gotit.pub (What is GotitPub?)
Huggingface Toggle
Hugging Face (What is Huggingface?)
ScienceCast Toggle
ScienceCast (What is ScienceCast?)
Demos
Replicate Toggle
Replicate (What is Replicate?)
Spaces Toggle
Hugging Face Spaces (What is Spaces?)
Spaces Toggle
TXYZ.AI (What is TXYZ.AI?)
Recommenders and Search Tools
Link to Influence Flower
Influence Flower (What are Influence Flowers?)
Core recommender toggle
CORE Recommender (What is CORE?)
IArxiv recommender toggle
IArxiv Recommender
(What is IArxiv?)
arXivLabs: experimental projects with community collaborators
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.
More from arXiv — Machine Learning
-
Dimensional Balance Improves Large Scale Spatiotemporal Prediction Performance
May 20
-
Robust Basis Spline Decoupling for the Compression of Transformer Models
May 20
-
HELLoRA: Hot Experts Layer-Level Low-Rank Adaptation for Mixture-of-Experts Models
May 20
-
UCCI: Calibrated Uncertainty for Cost-Optimal LLM Cascade Routing
May 20
Discussion (0)
Sign in to join the discussion. Free account, 30 seconds — email code or GitHub.
Sign in →No comments yet. Sign in and be the first to say something.