Mathematics > Optimization and Control
[Submitted on 3 Oct 2022 (v1), last revised 8 Jun 2024 (this version, v3)]
Title:A New Class of Path-Following Method for Time-Varying Optimization with Optimal Parametric Function
View PDF HTML (experimental)Abstract:In this paper, we consider a formulation of nonlinear constrained optimization problems.
We reformulate it as a time-varying optimization using continuous-time parametric functions
and derive a dynamical system for tracking the optimal solution.
We then re-parameterize the dynamical system to express it based on a linear combination of the parametric functions.
Calculus of variations is applied to optimize the parametric functions,
so that the optimality distance of the solution is minimized.
Accordingly, an iterative dynamic algorithm, named as OP-TVO,
is devised to find the solution with an efficient convergence rate.
We benchmark the performance of the proposed algorithm with the prediction-correction method (PCM)
from the optimality and computational complexity point-of-views.
The results show that OP-TVO can compete with PCM
for the optimization problem of interest,
which indicates it can be a promising approach to replace PCM for some time-varying optimization problems.
Furthermore, this work provides a novel paradigm for solving parametric dynamical system.
Submission history
From: Mohsen Amidzadeh [view email][v1] Mon, 3 Oct 2022 13:45:32 UTC (752 KB)
[v2] Wed, 8 Mar 2023 14:50:00 UTC (155 KB)
[v3] Sat, 8 Jun 2024 11:29:50 UTC (156 KB)
Current browse context:
math.OC
References & Citations
Bookmark
Bibliographic and Citation Tools
Bibliographic Explorer (What is the Explorer?)
Connected Papers (What is Connected Papers?)
Litmaps (What is Litmaps?)
scite Smart Citations (What are Smart Citations?)
Code, Data and Media Associated with this Article
alphaXiv (What is alphaXiv?)
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
DagsHub (What is DagsHub?)
Gotit.pub (What is GotitPub?)
Hugging Face (What is Huggingface?)
Papers with Code (What is Papers with Code?)
ScienceCast (What is ScienceCast?)
Demos
Recommenders and Search Tools
Influence Flower (What are Influence Flowers?)
CORE Recommender (What is CORE?)
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.