Let $x^* \in X$ and $\lambda^* \in \mathbb{R}^m$ satisfy \begin{align*} L(x^*, \lambda^*) = \inf_{x \in X} L(x, \lambda^*) \quad \text{and} \quad h(x^*) = b. \end{align*} Then $x^*$ is optimal for $(P)$, that is, $f(x^*) = \inf_{x \in X(b)} f(x)$, where $X(b) = \{x \in X : h(x) = b\}$ is the feasible set.