Optimization%20Theory

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Optimization Theory
Primal Optimization Problem

subject to
Primal Optimal Value
2
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