Projected Gradient Descent for Constrained Decision-Dependent Optimization

Fuente: arXiv
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Hauptverfasser: Wang, Zifan, Liu, Changxin, Parisini, Thomas, Zavlanos, Michael M., Johansson, Karl H.
Format: Preprint
Veröffentlicht: 2025
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author Wang, Zifan
Liu, Changxin
Parisini, Thomas
Zavlanos, Michael M.
Johansson, Karl H.
author_facet Wang, Zifan
Liu, Changxin
Parisini, Thomas
Zavlanos, Michael M.
Johansson, Karl H.
contents This paper considers the decision-dependent optimization problem, where the data distributions react in response to decisions affecting both the objective function and linear constraints. We propose a new method termed repeated projected gradient descent (RPGD), which iteratively projects points onto evolving feasible sets throughout the optimization process. To analyze the impact of varying projection sets, we show a Lipschitz continuity property of projections onto varying sets with an explicitly given Lipschitz constant. Leveraging this property, we provide sufficient conditions for the convergence of RPGD to the constrained equilibrium point. Compared to the existing dual ascent method, RPGD ensures continuous feasibility throughout the optimization process and reduces the computational burden. We validate our results through numerical experiments on a market problem and dynamic pricing problem.
format Preprint
id arxiv_https___arxiv_org_abs_2508_08856
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Projected Gradient Descent for Constrained Decision-Dependent Optimization
Wang, Zifan
Liu, Changxin
Parisini, Thomas
Zavlanos, Michael M.
Johansson, Karl H.
Optimization and Control
This paper considers the decision-dependent optimization problem, where the data distributions react in response to decisions affecting both the objective function and linear constraints. We propose a new method termed repeated projected gradient descent (RPGD), which iteratively projects points onto evolving feasible sets throughout the optimization process. To analyze the impact of varying projection sets, we show a Lipschitz continuity property of projections onto varying sets with an explicitly given Lipschitz constant. Leveraging this property, we provide sufficient conditions for the convergence of RPGD to the constrained equilibrium point. Compared to the existing dual ascent method, RPGD ensures continuous feasibility throughout the optimization process and reduces the computational burden. We validate our results through numerical experiments on a market problem and dynamic pricing problem.
title Projected Gradient Descent for Constrained Decision-Dependent Optimization
topic Optimization and Control
url https://arxiv.org/abs/2508.08856