Lecture: Decomposition Applications

Description

Lecture Description

Decomposition Applications, Rate Control Setup, Rate Control Problem, Rate Control Lagrangian, Aside: Utility Functions, Rate Control Dual, Dual Decomposition Rate Control Algorithm, Generating Feasible Flows, Convergence Of Primal And Dual Objectives, Maximum Capacity Violation, Single Commodity Network Flow Setup, Network Flow Problem, Network Flow Lagrangian, Network Flow Dual, Recovering Primal From Dual, Dual Decomposition Network Flow Algorithm, Electrical Network Analogy, Example: Minimum Queueing Delay, Optimal Flow, Convergence Of Dual Function, Convergence Of Primal Residual, Convergence Of Dual Variables, Aside: More Complicated Problems

Course Description

Continuation of Convex Optimization I.

Topics include: Subgradient, cutting-plane, and ellipsoid methods. Decentralized convex optimization via primal and dual decomposition. Alternating projections. Exploiting problem structure in implementation. Convex relaxations of hard problems, and global optimization via branch & bound. Robust optimization. Selected applications in areas such as control, circuit design, signal processing, and communications.

from course: Convex Optimization II