DOFFO_TR: a Decentralized Objective Function-Free Optimization method with Trust-Region
Abstract
In this paper, we propose a novel objective function-free trust-region method designed to solve optimization problems over decentralized networks. Unlike traditional approaches that often rely on stepsize tuning, our framework employs a function-free trust-region procedure that enables adaptive selection of the step length. Our approach accommodates first- and second-order models and eliminates the need to share local function values and gradients among agents, thereby enhancing privacy and computational efficiency. On the theoretical side, we establish provable iteration complexity guarantees that, for some variants, match those established for classical centralized trust-region methods. Numerical evaluations demonstrate that our approach achieves a favorable trade-off between performance and efficiency, requiring only moderate communication overhead compared to state-of-the-art methods in the literature.
Related
- Beyond Finite-Sum Optimization: A Primal-Dual Method for Decentralized Finite-Max Optimization
- A sequential quadratic programming method for optimization with expectation objective functions, deterministic inequality constraints and robust subproblems
- MPFA: A Pareto Front Approximation Method for Riemannian Bi-objective Optimization
- Surrogate-assisted multi-objective topology optimization design method for prefabricated large-span Suspen-Dome based on structural-mapping-method and improved-PGSA
- On solving integer bilevel optimization problems with a non-convex quadratic follower objective function using disjunctive cuts
BibTeX
@misc{bellavia2026doffotr,
title = {{DOFFO_TR: a Decentralized Objective Function-Free Optimization method with Trust-Region}},
author = {Stefania Bellavia and Greta Malaspina and Benedetta Morini},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.00878},
eprint = {2609.00878},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.00878},
}
RIS
TY - UNPB
TI - DOFFO_TR: a Decentralized Objective Function-Free Optimization method with Trust-Region
AU - Stefania Bellavia
AU - Greta Malaspina
AU - Benedetta Morini
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.00878
UR - https://arxiv.org/abs/2609.00878
AB - In this paper, we propose a novel objective function-free trust-region method designed to solve optimization problems over decentralized networks. Unlike traditional approaches that often rely on stepsize tuning, our framework employs a function-free trust-region procedure that enables adaptive selection of the step length. Our approach accommodates first- and second-order models and eliminates the need to share local function values and gradients among agents, thereby enhancing privacy and computational efficiency. On the theoretical side, we establish provable iteration complexity guarantees that, for some variants, match those established for classical centralized trust-region methods. Numerical evaluations demonstrate that our approach achieves a favorable trade-off between performance and efficiency, requiring only moderate communication overhead compared to state-of-the-art methods in the literature.
ER -