Optimization Theory Primal Optimization Problem subject to Primal

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 KKT Complementarity Condition

Optimization Theory Dual Lagrangian Function

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

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

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

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

Support Vector Machine (SVM) Linear SVM Prediction Testing dataset:

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

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

Support Vector Machine (SVM) Linear SVM: Separable case

Support Vector Machine (SVM) Linear SVM: Separable case

Support Vector Machine (SVM) Linear SVM: Separable case

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

Support Vector Machine (SVM) Linear SVM: Separable case

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

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

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

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

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

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

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