2015/11/08 by Víctor Valls, Valls, Víctor, Douglas J. Leith +1
Computer Science · Engineering · Mathematics · #Advanced MIMO Systems Optimization #Advanced Wireless Network Optimization #Cooperative Communication and Network Coding #FOS: Mathematics #Optimization and Control (math.OC) #math.OC
paper · pdf · doi:10.48550/arxiv.1511.02517
14 pages
arxiv created 2015/11/08 · openalex publication_date 2015/11/08 · arxiv updated 2015/11/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the use of approximate Lagrange multipliers and discrete actions in solving convex optimisation problems. We observe that descent, which can be ensured using a wide range of approaches (gradient, subgradient, Newton, etc.), is orthogonal to the choice of multipliers. Using the Skorokhod representation for a queueing process we show that approximate multipliers can be constructed in a number of ways. These observations lead to the generalisation of (i) essentially any descent method to encompass use of discrete actions and queues and (ii) max-weight scheduling to encompass new descent methods including those with unsynchronised updates such as block coordinate descent. This also allows consideration of communication delays and of updates at varying time-scales within the same clean and consistent framework.