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Financial Machine Learning / Margin Methods and Kernels

Derivation: The SVM Dual via Lagrangian Duality and the KKT Conditions

This note is the algebraic engine behind the previous lesson's Theorem 1: it works through, line by line, how the Lagrangian of the optimal margin classifier's primal problem is minimised over (w,b)(w,b) and reduces — after substitution — to the dual objective W(α)W(\alpha) stated (but not derived) previously.

In this lesson

  1. Setup
  2. Derivation (minimising the Lagrangian over ww and bb)
  3. Recovering the intercept b∗b^*
  4. Worked numerical check

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