# KKT form and Slater condition exercises

I just have learned a nice necessary and sufficient condition for convex optimization KKT form but i can't find exercises or examples for this. Can someone help me? ( some examples or exercies or book that have exercises about this)

Consider convex optimization problem (P):

minimize $f(x)$

subject to $g_i(x) \leq 0$ for $i=1,..,m$

$x \in \Omega$

Where $f: \mathbb{R}^n \to \mathbb{R}$ is convex function and $\Omega$ is a nonempty, convex set.

Slater's condition constraint qualification (CQ) holds in (P) if there exists $u \in \Omega$ such that $g_i(u)<0$ for all $i=1,..,m$.

Theorem: [Karush-Kuhn-Tucker Optimality Conditions in Convex Programming] Suppose that Slater's CQ holds in (P). Then $x^*$ is an optimal solution to (P) if and only if there exist nonnegative Lagrange multipliers $(\lambda_1,..,\lambda_m) \in \mathbb{R}^m$ such that

$$0 \in \partial f(x^*) + \sum_{i=1}^m \lambda_i \partial g_i(x^*) + N(x^*,\Omega)$$