Abstract
Distributed network optimization has been studied for well over a decade. However, we still do not have a good idea of how to design schemes that can simultaneously provide good performance across the dimensions of utility optimality, convergence speed, and delay. To address these challenges, in this paper, we propose a new algorithmic framework with all these metrics approaching optimality. The salient features of our new algorithm are three-fold: (i) fast convergence: it converges with only O(\log(1/\epsilon)) iterations that is the fastest speed among all the existing algorithms; (ii) low delay: it guarantees optimal utility with finite queue length; (iii) simple implementation: the control variables of this algorithm are based on virtual queues that do not require maintaining per-flow information. The new technique builds on a kind of inexact Uzawa method in the Alternating Directional Method of Multiplier, and provides a new theoretical path to prove global and linear convergence rate of such a method without requiring the full rank assumption of the constraint matrix.
- Eleftheria Athanasopoulou, Loc X Bui, Tianxiong Ji, R Srikant, and Alexander Stolyar. 2013. Back-pressure-based packet-by-packet adaptive routing in communication networks. IEEE/ACM Transactions on Networking (TON) 21, 1 (2013), 244--257. Google Scholar
Digital Library
- James H Bramble, Joseph E Pasciak, and Apostol T Vassilev. 1997. Analysis of the inexact Uzawa algorithm for saddle point problems. SIAM J. Numer. Anal. 34, 3 (1997), 1072--1092. Google Scholar
Digital Library
- Damek Davis and Wotao Yin. 2017. Faster convergence rates of relaxed Peaceman-Rachford and ADMM under regularity assumptions. Mathematics of Operations Research (2017).Google Scholar
- Wei Deng, Ming-Jun Lai, Zhimin Peng, and Wotao Yin. 2017. Parallel multi-block ADMM with O (1/k) convergence. Journal of Scientific Computing 71, 2 (2017), 712--736. Google Scholar
Digital Library
- Wei Deng and Wotao Yin. 2016. On the global and linear convergence of the generalized alternating direction method of multipliers. Journal of Scientific Computing 66, 3 (2016), 889--916. Google Scholar
Digital Library
- Defeng Sun Deren Han and Liwei Zhang. 2017. Linear Rate Convergence of the Alternating Direction Method of Multipliers for Convex Composite Programming. In Mathematics of Operation Research.Google Scholar
- Asen L Dontchev and R Tyrrell Rockafellar. 2009. Implicit functions and solution mappings. Springer Monogr. Math. (2009).Google Scholar
- John Duchi, Shai Shalev-Shwartz, Yoram Singer, and Tushar Chandra. 2008. Efficient projections onto the l 1-ball for learning in high dimensions. In Proceedings of the 25th international conference on Machine learning. ACM, 272--279. Google Scholar
Digital Library
- Atilla Eryilmaz and R Srikant. 2006. Joint congestion control, routing, and MAC for stability and fairness in wireless networks. IEEE Journal on Selected Areas in Communications 24, 8 (2006), 1514--1524. Google Scholar
Digital Library
- Daniel Gabay and Bertrand Mercier. 1976. A dual algorithm for the solution of nonlinear variational problems via finite element approximation. Computers & Mathematics with Applications 2, 1 (1976), 17--40.Google Scholar
Cross Ref
- Martin Grötschel, László Lovász, and Alexander Schrijver. 1981. The ellipsoid method and its consequences in combinatorial optimization. Combinatorica 1, 2 (1981), 169--197.Google Scholar
Cross Ref
- Martin Grötschel, László Lovász, and Lex Schrijver. 1993. Geometric algorithms and combinatorial optimization. Algorithms and Combinatorics 2 (1993), 1--362.Google Scholar
- Bingsheng He and Xiaoming Yuan. 2015. On non-ergodic convergence rate of Douglas--Rachford alternating direction method of multipliers. Numer. Math. 130, 3 (2015), 567--577. Google Scholar
Digital Library
- Alan J Hoffman. 2003. On approximate solutions of systems of linear inequalities. Selected Papers Of Alan J Hoffman: With Commentary (2003), 174--176.Google Scholar
- Longbo Huang and Michael J Neely. 2011. Delay reduction via Lagrange multipliers in stochastic network optimization. IEEE Trans. Automat. Control 56, 4 (2011), 842--857.Google Scholar
Cross Ref
- Martin Jaggi. 2013. Revisiting Frank-Wolfe: Projection-Free Sparse Convex Optimization.. In ICML (1). 427--435. Google Scholar
Digital Library
- Libin Jiang and JeanWalrand. 2010. A distributed CSMA algorithm for throughput and utility maximization in wireless networks. IEEE/ACM Transactions on Networking (ToN) 18, 3 (2010), 960--972. Google Scholar
Digital Library
- Srisankar Kunniyur and Rayadurgam Srikant. 2001. Analysis and design of an adaptive virtual queue (AVQ) algorithm for active queue management. In ACM SIGCOMM Computer Communication Review, Vol. 31. ACM, 123--134. Google Scholar
Digital Library
- Tianyi Lin, Shiqian Ma, and Shuzhong Zhang. 2015. On the global linear convergence of the admm with multiblock variables. SIAM Journal on Optimization 25, 3 (2015), 1478--1497.Google Scholar
Cross Ref
- Xiaojun Lin and Ness B Shroff. 2004. Joint rate control and scheduling in multihop wireless networks. In Decision and Control, 2004. CDC. 43rd IEEE Conference on, Vol. 2. IEEE, 1484--1489.Google Scholar
- Xiaojun Lin and Ness B Shroff. 2006. Utility maximization for communication networks with multipath routing. IEEE Trans. Automat. Control 51, 5 (2006), 766--781.Google Scholar
Cross Ref
- Xiaojun Lin, Ness B Shroff, and Rayadurgam Srikant. 2006. A tutorial on cross-layer optimization in wireless networks. IEEE Journal on Selected areas in Communications 24, 8 (2006), 1452--1463. Google Scholar
Digital Library
- Jia Liu. 2016. Achieving low-delay and fast-convergence in stochastic network optimization: A nesterovian approach. In Proceedings of the 2016 ACM SIGMETRICS International Conference on Measurement and Modeling of Computer Science. ACM, 221--234. Google Scholar
Digital Library
- Jia Liu, Atilla Eryilmaz, Ness B Shroff, and Elizabeth S Bentley. 2016. Heavy-ball: A new approach to tame delay and convergence in wireless network optimization. In Computer Communications, IEEE INFOCOM 2016-The 35th Annual IEEE International Conference on. IEEE, 1--9.Google Scholar
- Jia Liu, Ness B Shroff, Cathy H Xia, and Hanif D Sherali. 2016. Joint congestion control and routing optimization: An efficient second-order distributed approach. IEEE/ACM Transactions on Networking 24, 3 (2016), 1404 1420. Google Scholar
Digital Library
- Jia Liu, Cathy H Xia, Ness B Shroff, and Hanif D Sherali. 2013. Distributed cross-layer optimization in wireless networks: A second-order approach. In INFOCOM, 2013 Proceedings IEEE. IEEE, 2103--2111.Google Scholar
Cross Ref
- Michael J Neely, Eytan Modiano, and Charles E Rohrs. 2003. Power allocation and routing in multibeam satellites with time-varying channels. IEEE/ACM Transactions on Networking (TON) 11, 1 (2003), 138--152. Google Scholar
Digital Library
- Yurii Nesterov. 2009. Primal-dual subgradient methods for convex problems. Mathematical programming 120, 1 (2009), 221--259. Google Scholar
Digital Library
- R. J.-B. Wets R. T. Rockafellar. 1998. Variational analysis. (1998).Google Scholar
- Stephen M Robinson. 1981. Some continuity properties of polyhedral multifunctions. Mathematical Programming at Oberwolfach (1981), 206--214.Google Scholar
- R Tyrrell Rockafellar. 1997. Convex Analysis. (1997).Google Scholar
- Ralph Tyrell Rockafellar. 2015. Convex analysis. Princeton university press.Google Scholar
- Gaurav Sharma, Ravi R Mazumdar, and Ness B Shroff. 2006. On the complexity of scheduling in wireless networks. In Proceedings of the 12th annual international conference on Mobile computing and networking. ACM, 227--238. Google Scholar
Digital Library
- Alexander L Stolyar. 2005. Maximizing queueing network utility subject to stability: Greedy primal-dual algorithm. Queueing Systems 50, 4 (2005), 401--457. Google Scholar
Digital Library
- Leandros Tassiulas and Anthony Ephremides. 1992. Stability properties of constrained queueing systems and scheduling policies for maximum throughput in multihop radio networks. IEEE transactions on automatic control 37, 12 (1992), 1936--1948.Google Scholar
- ErminWei, Asuman Ozdaglar, and Ali Jadbabaie. 2013. A distributed Newton method for network utility maximization-- I: Algorithm. IEEE Trans. Automat. Control 58, 9 (2013), 2162--2175.Google Scholar
Cross Ref
- Hao Yu and Michael J Neely. 2017. A New Backpressure Algorithm for Joint Rate Control and Routing with Vanishing Utility Optimality Gaps and Finite Queue Lengths. arXiv preprint arXiv:1701.04519 (2017).Google Scholar
- Xiaoqun Zhang, Martin Burger, and Stanley Osher. 2011. A unified primal-dual algorithm framework based on Bregman iteration. Journal of Scientific Computing 46, 1 (2011), 20--46. Google Scholar
Digital Library
Index Terms
Towards Fast-Convergence, Low-Delay and Low-Complexity Network Optimization
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