Optimization Theory
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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

Primal Optimization Problem

subject to:

Primal Optimal Value:


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Optimization Theory

Convex Optimization Problem

subject to:

: convex functions


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Optimization Theory

Primal Lagrangian function

subject to:


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Optimization Theory

Kuhn-Tucker Theory

KKT Complementarity Condition


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Optimization Theory

Dual Lagrangian Function


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Optimization Theory

Dual Optimization problem

subject to:

subject to:

Primal

Dual

For convex optimization problem:


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Support Vector Machine (SVM)

  • SVM

  • Classification

  • Regression

  • Linear SVM

  • Nonlinear SVM


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Support Vector Machine (SVM)

  • Linear SVM

  • Training

  • Prediction


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Support Vector Machine (SVM)

  • Linear SVM Training

Training dataset:

Optimal Separating Hyperplane:


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Support Vector Machine (SVM)

  • Linear SVM Prediction

Testing dataset:


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Support Vector Machine (SVM)

  • Linear SVM: Separable case

  • The optimal hyperplane is obtained by maximizing the margin

  • Support vectors


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Support Vector Machine (SVM)

  • Linear SVM: Separable case

Primal Problem


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Support Vector Machine (SVM)

  • Linear SVM: Separable case


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Support Vector Machine (SVM)

  • Linear SVM: Separable case


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Support Vector Machine (SVM)

  • Linear SVM: Separable case


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Support Vector Machine (SVM)

  • Linear SVM: Separable case

Dual Problem


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Support Vector Machine (SVM)

  • Linear SVM: Separable case


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Support Vector Machine (SVM)

  • Linear SVM: Non-separable case


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Support Vector Machine (SVM)

  • Linear SVM: Non-separable case


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Support Vector Machine (SVM)

  • Linear SVM: Non-separable case


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Support Vector Machine (SVM)

  • Linear SVM: Non-separable case (Primal Problem)

Subject to:


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Support Vector Machine (SVM)

  • Linear SVM: Non-separable case (Primal Problem)


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Support Vector Machine (SVM)

  • Linear SVM: Non-Separable case


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Support Vector Machine (SVM)

  • Linear SVM: Non-separable case (Implementation)

Quadratic programming Problem