Stanford / Mathematics

Convergence Proof, Stopping Criterion

By Stephen Boyd | Convex Optimization II Lecture 3 of 18

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Lecture Description

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 Completion, Speeding Up Subgradient Methods, A Couple Of Speedup Algorithms, Subgradient Methods For Constrained Problems, Projected Subgradient Method, Linear Equality Constraints, Example: Least L_1-Norm

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.

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Course Index

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