Distributed Optimization in Networked Systems: Algorithms and Applications

Preface
Acknowledgments
Contents
List of Figures
1 Accelerated Algorithms for Distributed Convex Optimization
	1.1 Introduction
	1.2 Preliminaries
		1.2.1 Notation
		1.2.2 Model of Optimization Problem
		1.2.3 Communication Network
	1.3 Algorithm Development
		1.3.1 Centralized Nesterov Gradient Descent Method (CNGD)
		1.3.2 Directed Distributed Nesterov-Like Gradient Tracking (D-DNGT) Algorithm
		1.3.3 Related Methods
	1.4 Convergence Analysis
		1.4.1 Auxiliary Results
		1.4.2 Supporting Lemmas
		1.4.3 Main Results
		1.4.4 Discussion
	1.5 Numerical Examples
	1.6 Conclusion
	References
2 Projection Algorithms for Distributed Stochastic Optimization
	2.1 Introduction
	2.2 Preliminaries
		2.2.1 Notation
		2.2.2 Model of Optimization Problem
		2.2.3 Communication Network
	2.3 Algorithm Development
		2.3.1 Problem Reformulation
		2.3.2 Computation-Efficient Distributed Stochastic Gradient Algorithm
	2.4 Convergence Analysis
		2.4.1 Auxiliary Results
		2.4.2 Supporting Lemmas
		2.4.3 Main Results
		2.4.4 Discussion
	2.5 Numerical Examples
		2.5.1 Example 1: Performance Examination
		2.5.2 Example 2: Application Behavior
	2.6 Conclusion
	References
3 Proximal Algorithms for Distributed Coupled Optimization
	3.1 Introduction
	3.2 Preliminaries
		3.2.1 Notation
		3.2.2 Model of Optimization Problem
		3.2.3 Motivating Examples
		3.2.4 The Saddle-Point Reformulation
	3.3 Algorithm Development
		3.3.1 Unbiased Stochastic Average Gradient (SAGA)
		3.3.2 Distributed Stochastic Algorithm (VR-DPPD)
	3.4 Convergence Analysis
		3.4.1 Auxiliary Results
		3.4.2 Main Results
	3.5 Numerical Examples
		3.5.1 Example 1: Simulation on General Real Data
		3.5.2 Example 2: Simulation on Large-Scale Real Data
	3.6 Conclusion
	References
4 Event-Triggered Algorithms for Distributed Convex Optimization
	4.1 Introduction
	4.2 Preliminaries
		4.2.1 Notation
		4.2.2 Model of Optimization Problem
		4.2.3 Communication Networks
	4.3 Algorithm Development
		4.3.1 Distributed Subgradient Algorithm
	4.4 Convergence Analysis
		4.4.1 Auxiliary Results
		4.4.2 Main Results
	4.5 Numerical Examples
	4.6 Conclusion
	References
5 Event-Triggered Acceleration Algorithms for Distributed Stochastic Optimization
	5.1 Introduction
	5.2 Preliminaries
		5.2.1 Notation
		5.2.2 Model of Optimization Problem
		5.2.3 Communication Network
	5.3 Algorithm Development
		5.3.1 Event-Triggered Communication Strategy
		5.3.2 Event-Triggered Distributed Accelerated Stochastic Gradient Algorithm (ET-DASG)
	5.4 Convergence Analysis
		5.4.1 Auxiliary Results
		5.4.2 Supporting Lemmas
		5.4.3 Main Results
	5.5 Numerical Examples
		5.5.1 Example 1: Logistic Regression
		5.5.2 Example 2: Energy-based Source Localization
	5.6 Conclusion
	References
6 Accelerated Algorithms for Distributed Economic Dispatch
	6.1 Introduction
	6.2 Preliminaries
		6.2.1 Notation
		6.2.2 Model of Optimization Problem
		6.2.3 Communication Network
		6.2.4 Centralized Lagrangian Method
	6.3 Algorithm Development
		6.3.1 Directed Distributed Lagrangian Momentum Algorithm
		6.3.2 Related Methods
	6.4 Convergence Analysis
		6.4.1 Auxiliary Results
		6.4.2 Main Results
	6.5 Numerical Examples
		6.5.1 Case Study 1: EDP on IEEE 14-Bus Test Systems
		6.5.2 Case Study 2: EDP on IEEE 118-Bus Test Systems
		6.5.3 Case Study 3: The Application to Dynamical EDPs
		6.5.4 Case Study 4: Comparison with Related Methods
	6.6 Conclusion
	References
7 Primal–Dual Algorithms for Distributed Economic Dispatch
	7.1 Introduction
	7.2 Preliminaries
		7.2.1 Notation
		7.2.2 Model of Optimization Problem
		7.2.3 Communication Network
	7.3 Algorithm Development
		7.3.1 Dual Problem
		7.3.2 Distributed Primal–Dual Gradient Algorithm
	7.4 Convergence Analysis
		7.4.1 Small Gain Theorem
		7.4.2 Supporting Lemmas
		7.4.3 Main Results
	7.5 Numerical Examples
		7.5.1 Example 1: EDP on the IEEE 14-Bus Test Systems
		7.5.2 Example 2: Demand Response for Time-Varying Supplies
	7.6 Conclusion
	References
8 Event-Triggered Algorithms for Distributed Economic Dispatch
	8.1 Introduction
	8.2 Preliminaries
		8.2.1 Notation
		8.2.2 Nomenclature
		8.2.3 Model of Optimization Problem
		8.2.4 Communication Network
	8.3 Algorithm Development
		8.3.1 Problem Reformulation
		8.3.2 Event-Triggered Control Scheme
			8.3.2.1 Event-Triggered Distributed Accelerated Primal–Dual Algorithm (ET-DAPDA)
	8.4 Convergence Analysis
		8.4.1 Supporting Lemmas
		8.4.2 Main Results
		8.4.3 The Exclusion of Zeno-Like Behavior
	8.5 Numerical Examples
		8.5.1 Example 1: EDP on the IEEE 14-Bus System
		8.5.2 Example 2: EDP on Large-Scale Networks
		8.5.3 Example 3: Comparison with Related Methods
	8.6 Conclusion
	References
9 Privacy Preserving Algorithms for Distributed Online Learning
	9.1 Introduction
	9.2 Preliminaries
		9.2.1 Notation
		9.2.2 Model of Optimization Problem
		9.2.3 Communication Network
	9.3 Algorithm Development
		9.3.1 Differential Privacy Strategy
		9.3.2 Differentially Private Distributed Online Algorithm
	9.4 Main Results
		9.4.1 Differential Privacy Analysis
		9.4.2 Logarithmic Regret
		9.4.3 Square-Root Regret
		9.4.4 Robustness to Communication Delays
	9.5 Numerical Examples
	9.6 Conclusion
	References