What is the dual optimization objective of SVM?

The dual objective reformulates SVM optimization in terms of Lagrange multipliers based on dot products between data points.

The dual form maximizes a convex quadratic function over Lagrange multipliers (α). It depends only on inner products x_i · x_j, enabling kernel methods. The constraints ensure α_i ≥ 0 and sum of α_i y_i = 0. Only non-zero α values correspond to support vectors. This formulation is computationally critical for high-dimensional feature mappings.