# Convex Optimization II

- Institution: Stanford University
- Department: Electrical Engineering
- Teacher: Stephen Boyd
- Level: Undergraduate
- Language: English
- Subjects: Engineering
- Source: [Stanford Engineering Everywhere](https://see.stanford.edu/Course/EE364B)
- Licence: [CC BY-NC-SA 4.0](http://creativecommons.org/licenses/by-nc-sa/4.0/legalcode) (Non-commercial use only.)
- Syllabus: [at the source](https://see.stanford.edu/materials/lsocoee364b/Syllabus.pdf)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

Continuation of Convex Optimization I. 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. Course requirements include a substantial project.

Prerequisites: Convex Optimization I

## Lectures

1. [Course Logistics, Course Organization, Course Topics, Subgradients, Basic Inequality, Subgradient Of A Function, Subdifferential, Subgradient Calculus, Some Basic Rules (For Subgradient Calculus), Pointwise Supremum, Weak Rule For…](https://invisiblenetwork.ai/learn/stanford/ee364b/4f93db64c4bb), 1 h 2 min (Video)
2. [Recap: Subgradients, Subgradients And Sublevel Sets, Quasigradients, Optimality Conditions – Unconstrained, Example: Piecewise Linear Minimization, Optimality Conditions – Constrained, Directional Derivative And Subdifferential, Descent…](https://invisiblenetwork.ai/learn/stanford/ee364b/1d81cfa40f25), 1 h 7 min (Video)
3. [Convergence Proof, Stopping Criterion, Example: Piecewise Linear Minimization, Optimal Step Size When F* Is Known, Finding A Point In The Intersection Of Convex Sets, Alternating Projections, Example: Positive Semidefinite Matrix…](https://invisiblenetwork.ai/learn/stanford/ee364b/218fe8a56585), 1 h 15 min (Video)
4. [Project Subgradient For Dual Problem, Subgradient Of Negative Dual Function, Example (Strictly Convex Quadratic Function Over Unit Box), Subgradient Method For Constrained Optimization, Convergence, Example: Inequality Form LP, Stochastic…](https://invisiblenetwork.ai/learn/stanford/ee364b/a48869c06e9b), 1 h 19 min (Video)
5. [Stochastic Programming, Variations (Of Stochastic Programming), Expected Value Of A Convex Function, Example: Expected Value Of Piecewise Linear Function, On-Line Learning And Adaptive Signal Processing, Example: Mean-Absolute Error…](https://invisiblenetwork.ai/learn/stanford/ee364b/6e8cd4da71ca), 1 h 16 min (Video)
6. [Addendum: Hit-And-Run CG Algorithm, Maximum Volume Ellipsoid Method, Chebyshev Center Method, Analytic Center Cutting-Plane Method, Extensions (Of Cutting-Plane Methods), Dropping Constraints, Epigraph Cutting-Plane Method, PWL Lower…](https://invisiblenetwork.ai/learn/stanford/ee364b/f6feb5079b10), 1 h 12 min (Video)
7. [Example: Piecewise Linear Minimization, ACCPM With Constraint Dropping, Epigraph ACCPM, Motivation (For Ellipsoid Method), Ellipsoid Algorithm For Minimizing Convex Function, Properties Of Ellipsoid Method, Example (Using Ellipsoid…](https://invisiblenetwork.ai/learn/stanford/ee364b/a2b0a87545c6), 1 h 14 min (Video)
8. [Recap: Ellipsoid Method, Improvements (To Ellipsoid Method), Proof Of Convergence, Interpretation Of Complexity, Deep Cut Ellipsoid Method, Ellipsoid Method With Deep Objective Cuts, Inequality Constrained Problems, Stopping Criterion,…](https://invisiblenetwork.ai/learn/stanford/ee364b/209b973ce293), 1 h 11 min (Video)
9. [Comments: Latex Typesetting Style, Recap: Primal Decomposition, Dual Decomposition, Dual Decomposition Algorithm, Finding Feasible Iterates, Interpretation, Decomposition With Constraints, Primal Decomposition (With Constraints)…](https://invisiblenetwork.ai/learn/stanford/ee364b/e6a9693559e2), 1 h 10 min (Video)
10. [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…](https://invisiblenetwork.ai/learn/stanford/ee364b/9b7212564a42), 1 h 17 min (Video)
11. [Sequential Convex Programming, Methods For Nonconvex Optimization Problems, Sequential Convex Programming (SCP), Basic Idea Of SCP, Trust Region, Affine And Convex Approximations Via Taylor Expansions, Particle Method, Fitting Affine Or…](https://invisiblenetwork.ai/learn/stanford/ee364b/7b9759ef2819), 1 h 16 min (Video)
12. [Recap: 'Difference Of Convex' Programming, Alternating Convex Optimization, Nonnegative Matrix Factorization, Comment: Nonconvex Methods, Conjugate Gradient Method, Three Classes Of Methods For Linear Equations, Symmetric Positive…](https://invisiblenetwork.ai/learn/stanford/ee364b/d53016e1238c), 1 h 13 min (Video)
13. [Recap: Conjugate Gradient Method, Recap: Krylov Subspace, Spectral Analysis Of Krylov Sequence, A Bound On Convergence Rate, Convergence, Residual Convergence, CG Algorithm, Efficient Matrix-Vector Multiply, Shifting, Preconditioned…](https://invisiblenetwork.ai/learn/stanford/ee364b/920019761902), 1 h 15 min (Video)
14. [Methods (Truncated Newton Method), Convergence Versus Iterations, Convergence Versus Cumulative CG Steps, Truncated PCG Newton Method, Truncated Newton Interior-Point Methods, Network Rate Control, Dual Rate Control Problem, Primal-Dual…](https://invisiblenetwork.ai/learn/stanford/ee364b/06b44306973a), 1 h 13 min (Video)
15. [Recap: Example: Minimum Cardinality Problem, Interpretation As Convex Relaxation, Interpretation Via Convex Envelope, Weighted And Asymmetric L_1 Heuristics, Regressor Selection, Sparse Signal Reconstruction, L_1-Norm Methods For…](https://invisiblenetwork.ai/learn/stanford/ee364b/fcc2a3360a62), 1 h 3 min (Video)
16. [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…](https://invisiblenetwork.ai/learn/stanford/ee364b/77536947572a), 1 h 19 min (Video)
17. [Stochastic Model Predictive Control, Causal State-Feedback Control, Stochastic Finite Horizon Control, 'Solution' Via Dynamic Programming, Independent Process Noise, Linear Quadratic Stochastic Control, Certainty Equivalent Model…](https://invisiblenetwork.ai/learn/stanford/ee364b/5b80ad01e4b7), 1 h 17 min (Video)
18. [Announcements, Recap: Branch And Bound Methods, Basic Idea, Unconstrained, Nonconvex Minimization, Lower And Upper Bound Functions, Branch And Bound Algorithm, Comment: Picture Of Branch And Bound Algorithm In R^2, Comment: Binary Tree,…](https://invisiblenetwork.ai/learn/stanford/ee364b/d94b374a6d7c), 1 h 19 min (Video)