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Optimization Theory

Optimization Theory. Primal Optimization Problem. subject to:. Primal Optimal Value:. Optimization Theory. Convex Optimization Problem. subject to:. : convex functions. Optimization Theory. Primal Lagrangian function. subject to:. Optimization Theory. Kuhn-Tucker Theory.

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Optimization Theory

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  1. Optimization Theory Primal Optimization Problem subject to: Primal Optimal Value:

  2. Optimization Theory Convex Optimization Problem subject to: : convex functions

  3. Optimization Theory Primal Lagrangian function subject to:

  4. Optimization Theory Kuhn-Tucker Theory KKT Complementarity Condition

  5. Optimization Theory Dual Lagrangian Function

  6. Optimization Theory Dual Optimization problem subject to: subject to: Primal Dual For convex optimization problem:

  7. Support Vector Machine (SVM) • SVM • Classification • Regression • Linear SVM • Nonlinear SVM

  8. Support Vector Machine (SVM) • Linear SVM • Training • Prediction

  9. Support Vector Machine (SVM) • Linear SVM Training Training dataset: Optimal Separating Hyperplane:

  10. Support Vector Machine (SVM) • Linear SVM Prediction Testing dataset:

  11. Support Vector Machine (SVM) • Linear SVM: Separable case • The optimal hyperplane is obtained by maximizing the margin • Support vectors

  12. Support Vector Machine (SVM) • Linear SVM: Separable case Primal Problem

  13. Support Vector Machine (SVM) • Linear SVM: Separable case

  14. Support Vector Machine (SVM) • Linear SVM: Separable case

  15. Support Vector Machine (SVM) • Linear SVM: Separable case

  16. Support Vector Machine (SVM) • Linear SVM: Separable case Dual Problem

  17. Support Vector Machine (SVM) • Linear SVM: Separable case

  18. Support Vector Machine (SVM) • Linear SVM: Non-separable case

  19. Support Vector Machine (SVM) • Linear SVM: Non-separable case

  20. Support Vector Machine (SVM) • Linear SVM: Non-separable case

  21. Support Vector Machine (SVM) • Linear SVM: Non-separable case (Primal Problem) Subject to:

  22. Support Vector Machine (SVM) • Linear SVM: Non-separable case (Primal Problem)

  23. Support Vector Machine (SVM) • Linear SVM: Non-Separable case

  24. Support Vector Machine (SVM) • Linear SVM: Non-separable case (Implementation) Quadratic programming Problem

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