Primal and Dual Perspective for Linear SVM

May 28, 2026

Mathematical Foundations for Machine Learning

MFML, SVM, Linear SVM, Primal, Dual, Support Vectors, Hinge Loss

Primal and Dual Perspective for Linear SVM #

A linear Support Vector Machine finds a hyperplane that separates two classes with the maximum possible margin.

The primal view gives the direct geometric optimisation problem. The dual view rewrites the problem using Lagrange multipliers and reveals why only support vectors matter.

Key takeaway: Linear SVM maximises the margin by minimising
\( \frac{1}{2}\|w\|^2 \)
subject to correct-classification constraints. The dual solution expresses ( w )