Chapter 1 Introduction
1.1 Distributed optimization
1.1.1 Distributed deterministic optimization
1.1.2 Distributed stochastic optimization
1.2 Distributed machine learning
1.2.1 Distributed regression problem
1.2.2 Distributed classification problem
1.2.3 Distributed clustering problems
1.3 Structure and work of this book
Chapter 2 Preliminaries
2.1 Conve x analysis
2.1.1 Euclidean norm inequalities
2.1.2 Lipschitz continuous gradient
2.2 Probability theory
Chapter 3 Distributed Stochastic Sub-gradient Descent Algorithm
3.1 Distributed stochastic sub-gradient descent algorithm for conve x optimization
3.1.1 Background
3.1.2 Problem, algorithm and assumptions
3.1.3 Basic relations
3.1.4 Convergence in mean
3.1.5 Almost sure and mean square convergence
3.2 Distributed stochastic sub-gradient descent algorithm for regression estimation with incomplete data
3.2.1 Background
3.2.2 Problem form ulation
3.2.3 Distributed adaptive gradient-based algorithm
3.2.4 Main results of DAGA
3.2.5 Simulations
3.2.6 Conclusion
3.3 Distributed classification learning based on nonlinear vector support machines for switching networks
3.3.1 Background
3.3.2 Preliminary and SVM formulation
3.3.3 Distributed nonlinear SVM learning
3.3.4 Distributed stochastic sub-gradient based SVM algorithm
3.3.5 Simulations
3.3.6 Conclusion
Chapter 4 Distributed Mirror-descent Algorithm
4.1 Distributed stochastic mirror descent algorithm over time-varying network
4.1.1 Background
4.1.2 Preliminaries and assumptions
4.1.3 Distributed stochastic mirror descent algorithm
4.1.4 Main result
4.1.5 Simulation
4.1.6 Conclusions
4.2 A Stochastic mirror-descent algorithm for solving AXB=C over an multi-agent system
4.2.1 Background
4.2.2 Preliminaries
4.2.3 Problem form ulation and algorithm design
4.2.4 Main result
4.2.5 Simulation
4.2.6 Conclusions
