# Course - Convex Optimization II

Course Level: Master

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.n
Model Predictive Control, Linear Time-Invariant Convex Optimal Control, Greedy Control, 'Solution' Via Dynamic Programming, Linear Quadratic Regulator, Finite Horizon Approximation, Cost Versus Horizon, Trajectories, Model Predictive Control (MPC), MPC Performance Versus Horizon, MPC Trajectories, Variations On MPC, Explicit MPC, MPC Problem Structure, Fast MPC, Supply Chain Management, Constraints And Objective, MPC And Optimal Trajectories, Variations On Optimal Control Problem

Prerequisites
• Lecture 1 - Basic Rules for Subgradient Calculus
• Lecture 2 - Recap; Subgradients
• Lecture 3 - Convergence Proof, Stopping Criterion
• Lecture 4 - Project Subgradient For Dual Problem
• Lecture 5 - Stochastic Programming
• Lecture 6 - Addendum; Hit-And-Run CG Algorithm
• Lecture 7 - Example; Piecewise Linear Minimization
• Lecture 8 - Recap; Ellipsoid Method
• Lecture 9 - Comments; Latex Typesetting Style
• Lecture 10 - Decomposition Applications
• Lecture 11 - Sequential Convex Programming
• Lecture 12 - Recap; 'Difference Of Convex' Programming
• Lecture 13 - Recap; Conjugate Gradient Method
• Lecture 14 - Methods (Truncated Newton Method)
• Lecture 15 - Recap; Example; Minimum Cardinality Problem
• Lecture 16 - Model Predictive Control
• Lecture 17 - Stochastic Model Predictive Control
• Lecture 18 - Recap; Branch And Bound Methods, Basic Idea, Unconstrained, Nonconvex Minimization