Mathematical Preliminaries for SVM
May 28, 2026Mathematical Preliminaries for SVM #
Support Vector Machines use optimisation, geometry and kernels. Before deriving SVM, we need constrained optimisation, Lagrange multipliers, primal and dual problems, KKT conditions, hyperplanes and kernel functions.
Key takeaway: SVM is built on constrained optimisation. The hard-margin SVM primal problem is a quadratic optimisation problem with linear inequality constraints. The dual problem uses Lagrange multipliers and leads naturally to support vectors and kernels.