Block coordinate descent for joint delay-energy optimization in multi-hop D2D networks

2026-06-07

AI Summary

This study addresses the challenge of jointly optimizing delay and energy consumption in multihop device-to-device (D2D) networks, where tight coupling between routing decisions and physical-layer resource allocation complicates optimization. The authors propose a block coordinate descent framework that jointly optimizes routing, transmit power, and bandwidth allocation to minimize both the worst-case end-to-end delay and total energy consumption. Key innovations include a matrix-free Frank-Wolfe algorithm (MF-FW) for efficient near-optimal routing and a low-rank primal-dual interior-point method (LR-PDIPM) enhanced with Sherman-Morrison formulae and time-domain transformations to enable a parallel dual-ascent strategy that guarantees global convergence. Experimental results demonstrate that LR-PDIPM reduces total energy consumption by up to 9.14× and improves energy efficiency by an order of magnitude, while MF-FW computes solutions within seconds with a worst-case delay only 3.78× worse than the optimal.

Abstract

In multi-hop device-to-device (D2D) networks, the optimization of network-level metrics is particularly difficult due to the tight coupling between network-layer routing and physical-layer resource allocation. Departing from traditional average-performance metrics, this paper addresses the joint optimization of routing paths, transmission power, and bandwidth allocation. We formulate a generalized cost function to minimize the maximum transmission time (i.e., the bottleneck delay) alongside the total energy consumption. To tackle the resulting highly non-convex formulation, we propose a novel block coordinate descent (BCD) framework. At the network layer, we develop two adaptive routing algorithms: a matrix-free Frank-Wolfe (MF-FW) algorithm for fast execution in dense topologies, and a low-rank primal-dual interior-point method (LR-PDIPM) that bypasses dense matrix inversions via the Sherman-Morrison formula for high-precision solutions. At the physical layer, we design a parallel dual ascent algorithm leveraging a time-domain perspective transformation to solve the resource allocation subproblem to global optimality. The proposed BCD framework is proven to converge to an ε-neighborhood of a stationary point. Through comprehensive experiments, the proposed BCD framework establishes its superiority in achieving the optimal delay-energy trade-off. Specifically, the LR-PDIPM variant achieves a maximum 9.14-fold reduction in total energy consumption and up to an order of magnitude improvement in energy efficiency, while maintaining a bounded maximum delay gap (up to 3.78-fold) relative to the best baseline. Meanwhile, the warm-start MF-FW variant identifies near-optimal solutions in mere seconds, serving as a highly practical engineering approach.

Problem

• multi-hop D2D networks
• joint delay-energy optimization
• routing and resource allocation
• bottleneck delay
• energy consumption

Innovation

• block coordinate descent
• joint delay-energy optimization
• adaptive routing
• resource allocation
• multi-hop D2D networks