Teaching
Distributed Optimization and Control on Networks
Course Outline:
1. Basics on Optimization(a) Introduction to optimization: Unconstrained optimization, Optimality conditions, Gradient methods, Newton's method, Optimization over convex sets, Gradient projection methods.(b) Lagrange Multiplier Theory and Algorithms: Necessary and sufficient conditions (KKT), Barrier and interior-point methods, Penalty and augmented Lagrangian methods.(c) Duality and Convex Optimization: The dual problem, The weak duality theorem, Primal and dual optimal solutions, Dual derivative, and subgradients.
2. Graph Theoretic Methods in Networks(a) Introduction to Multiagent Networks: Modeling multiagent systems, Foundations of graph theory, Algebraic and spectral graph theory.(b) The Agreement Protocol: The consensus equation on undirected and directed graphs, discrete consensus equation and properties of stochastic matrices, constrained consensus algorithms.
3. Consensus-Based Optimization(a) Distributed Optimization Problem: Network optimization, multiagent networks problems, resource allocation problems.(b) Distributed Subgradient Method: Definitions, Convergent results, algorithms, applications.
4. D-ADMM(a) Alternating Direction Method of Multipliers: A way to ADMM, Dualization and decomposable functions, Augmented Lagrangian(b) Distributed ADMM: Parallel, asynchronous, distributed, and decentralized ADMM, Examples, and Algorithms.
