Time-Varying Optimization with Optimal Parametric Functions

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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.
Original languageEnglish
Title of host publication2023 62nd IEEE Conference on Decision and Control (CDC)
PublisherIEEE
Pages2300-2305
Number of pages6
ISBN (Print)979-8-3503-0125-0
DOIs
Publication statusPublished - 15 Dec 2023
MoE publication typeA4 Conference publication
EventIEEE Conference on Decision and Control - Marina Bay Sands, Singapore, Singapore
Duration: 13 Dec 202315 Dec 2023
Conference number: 62
https://cdc2023.ieeecss.org/

Publication series

NameProceedings of the IEEE Conference on Decision & Control
ISSN (Electronic)2576-2370

Conference

ConferenceIEEE Conference on Decision and Control
Abbreviated titleCDC
Country/TerritorySingapore
CitySingapore
Period13/12/202315/12/2023
Internet address

Keywords

  • Phase change materials
  • Heuristic algorithms
  • Prediction algorithms
  • Minimization
  • Iterative algorithms
  • Trajectory
  • Dynamical systems

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