A switching proximal gradient method for constrained difference-of-convex optimization problems
Abstract
We study difference-of-convex optimization problems with several composite inequality constraints and develop a majorization-guided switching proximal gradient (MGSPG) method. Specifically, at each feasible outer point, quadratic majorization and linearization yield a strongly convex composite surrogate problem. To solve this surrogate approximately, we employ a switching proximal gradient (SPG) method, which takes a proximal gradient step for the objective when the current point is nearly feasible and for a most violated constraint otherwise. This construction requires neither projection onto the joint surrogate feasible set nor multiplier computation. By establishing a common invariant ball and using an increasing weight argument, we obtain an O(τ−1) inner complexity bound for SPG. Building on this bound, we show that, under boundedness of the feasible level set and a uniform Slater condition for the surrogates, MGSPG finds an ε-KKT point in O(ε−2) outer iterations and O(ε−4) selected component proximal gradient updates. Numerical experiments on SCAD-constrained and groupwise-constrained regression problems demonstrate the viability and computational efficiency of our method compared with existing optimization algorithms.
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BibTeX
@misc{liu2026switching,
title = {{A switching proximal gradient method for constrained difference-of-convex optimization problems}},
author = {Yuncheng Liu and Chuangliang Zhang and Bo Yang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.37362},
eprint = {2610.37362},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.37362},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A switching proximal gradient method for constrained difference-of-convex optimization problems
AU - Yuncheng Liu
AU - Chuangliang Zhang
AU - Bo Yang
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2610.37362
UR - https://arxiv.org/abs/2610.37362
AB - We study difference-of-convex optimization problems with several composite inequality constraints and develop a majorization-guided switching proximal gradient (MGSPG) method. Specifically, at each feasible outer point, quadratic majorization and linearization yield a strongly convex composite surrogate problem. To solve this surrogate approximately, we employ a switching proximal gradient (SPG) method, which takes a proximal gradient step for the objective when the current point is nearly feasible and for a most violated constraint otherwise. This construction requires neither projection onto the joint surrogate feasible set nor multiplier computation. By establishing a common invariant ball and using an increasing weight argument, we obtain an O(τ^−1) inner complexity bound for SPG. Building on this bound, we show that, under boundedness of the feasible level set and a uniform Slater condition for the surrogates, MGSPG finds an ε-KKT point in O(ε^−2) outer iterations and O(ε^−4) selected component proximal gradient updates. Numerical experiments on SCAD-constrained and groupwise-constrained regression problems demonstrate the viability and computational efficiency of our method compared with existing optimization algorithms.
ER -