A constraint dissolving method for generally constrained optimization over a nonconvex set
Abstract
This manuscript studies a constraint dissolving method for solving optimization problems with general constraints, comprising an abstract constraint G(x) \in C and a potentially nonconvex geometric constraint x \in D, which, to the best of our knowledge, is the first constraint dissolving type method applicable to this general setting. More specifically, we introduce an auxiliary variable s to decouple G(x) \in C into G(x) = s and s \in C, and construct the constraint dissolving mapping acting jointly on both variables. We then propose a penalty-based constraint dissolving method, in which the penalty parameter is updated adaptively according to the feasibility error. Under mild conditions, every accumulation point is Mordukhovich-stationary. By a specific choice of the constraint dissolving mapping, every accumulation point is guaranteed to be feasible, which stands in contrast to standard penalty-type methods in nonconvex settings. Numerical experiments on Rosenbrock, portfolio, and MAXCUT problems demonstrate the effectiveness of the proposed method against the augmented Lagrangian and the penalty decomposition methods.
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BibTeX
@misc{liu2026constraint,
title = {{A constraint dissolving method for generally constrained optimization over a nonconvex set}},
author = {Pengjie Liu and Haonan Shen and Xiaoxi Jia},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.04954},
eprint = {2611.04954},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.04954},
note = {CC0},
}
RIS
TY - UNPB
TI - A constraint dissolving method for generally constrained optimization over a nonconvex set
AU - Pengjie Liu
AU - Haonan Shen
AU - Xiaoxi Jia
PY - 2026
DA - 2026/11/03
PB - arXiv
DO - 10.48550/arxiv.2611.04954
UR - https://arxiv.org/abs/2611.04954
AB - This manuscript studies a constraint dissolving method for solving optimization problems with general constraints, comprising an abstract constraint G(x) \in C and a potentially nonconvex geometric constraint x \in D, which, to the best of our knowledge, is the first constraint dissolving type method applicable to this general setting. More specifically, we introduce an auxiliary variable s to decouple G(x) \in C into G(x) = s and s \in C, and construct the constraint dissolving mapping acting jointly on both variables. We then propose a penalty-based constraint dissolving method, in which the penalty parameter is updated adaptively according to the feasibility error. Under mild conditions, every accumulation point is Mordukhovich-stationary. By a specific choice of the constraint dissolving mapping, every accumulation point is guaranteed to be feasible, which stands in contrast to standard penalty-type methods in nonconvex settings. Numerical experiments on Rosenbrock, portfolio, and MAXCUT problems demonstrate the effectiveness of the proposed method against the augmented Lagrangian and the penalty decomposition methods.
ER -