An Adaptive Proximal Inexact Gradient Framework and Its Application to Per-Antenna Constrained Joint Beamforming and Compression Design

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Main Authors: Fan, Xilai, Jiang, Bo, Liu, Ya-Feng
Format: Preprint
Published: 2025
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author Fan, Xilai
Jiang, Bo
Liu, Ya-Feng
author_facet Fan, Xilai
Jiang, Bo
Liu, Ya-Feng
contents In this paper, we propose an adaptive proximal inexact gradient (APIG) framework for solving a class of nonsmooth composite optimization problems involving function and gradient errors. Unlike existing inexact proximal gradient methods, the proposed framework introduces a new line search condition that jointly adapts to function and gradient errors, enabling adaptive stepsize selection while maintaining theoretical guarantees. Specifically, we prove that the proposed framework achieves an $ε$-stationary point within $\mathcal{O}(ε^{-2})$ iterations for nonconvex objectives and an $ε$-optimal solution within $\mathcal{O}(ε^{-1})$ iterations for convex cases, matching the best-known complexity in this context. We then custom-apply the APIG framework to an important signal processing problem: the joint beamforming and compression problem (JBCP) with per-antenna power constraints (PAPCs) in cooperative cellular networks. This customized application requires careful exploitation of the problem's special structure such as the tightness of the semidefinite relaxation (SDR) and the differentiability of the dual. Numerical experiments demonstrate the superior performance of our custom-application over state-of-the-art benchmarks for the JBCP.
format Preprint
id arxiv_https___arxiv_org_abs_2504_01721
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle An Adaptive Proximal Inexact Gradient Framework and Its Application to Per-Antenna Constrained Joint Beamforming and Compression Design
Fan, Xilai
Jiang, Bo
Liu, Ya-Feng
Information Theory
Signal Processing
Optimization and Control
In this paper, we propose an adaptive proximal inexact gradient (APIG) framework for solving a class of nonsmooth composite optimization problems involving function and gradient errors. Unlike existing inexact proximal gradient methods, the proposed framework introduces a new line search condition that jointly adapts to function and gradient errors, enabling adaptive stepsize selection while maintaining theoretical guarantees. Specifically, we prove that the proposed framework achieves an $ε$-stationary point within $\mathcal{O}(ε^{-2})$ iterations for nonconvex objectives and an $ε$-optimal solution within $\mathcal{O}(ε^{-1})$ iterations for convex cases, matching the best-known complexity in this context. We then custom-apply the APIG framework to an important signal processing problem: the joint beamforming and compression problem (JBCP) with per-antenna power constraints (PAPCs) in cooperative cellular networks. This customized application requires careful exploitation of the problem's special structure such as the tightness of the semidefinite relaxation (SDR) and the differentiability of the dual. Numerical experiments demonstrate the superior performance of our custom-application over state-of-the-art benchmarks for the JBCP.
title An Adaptive Proximal Inexact Gradient Framework and Its Application to Per-Antenna Constrained Joint Beamforming and Compression Design
topic Information Theory
Signal Processing
Optimization and Control
url https://arxiv.org/abs/2504.01721