Derive the hard-margin SVM dual

ProofGraduate⏱ 3 hoursClassical MLsvmduallagrangianderivationflagship

Problem

Starting from $\min\frac12\|w\|_2^2$ subject to $y_i(\langle w,x_i\rangle+b)\ge1$ , derive the dual

\max_{\alpha\ge0,\ \alpha^\top y=0}\ \sum_i\alpha_i - \frac12\sum_{i,j}\alpha_i\alpha_jy_iy_j\langle x_i,x_j\rangle .

Explain where the equality constraint comes from, verify strong duality, and give the recovery formulas for $w^\star$ and $b^\star$ .

Write a complete argument. Every inequality you use should be one you could state precisely.

Opening this before you have a real attempt on paper is the fastest way to feel like you understand something you cannot reproduce.

Problem	Field	Type	Difficulty	Time
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