General Optimization Problem

We want to optimize the Objective Function, $f$.

$$mi{n}_{x\in \mathbb{R}}f(x)\text{ subject to }\{\begin{array}{ll}{c}_i=0& i\in \mathcal{E}\\ c_i(x)\ge 0& i\in \mathcal{I}\end{array}$$

Where $c_i,i\in \mathcal{E}$ are the Equality Constraint and $c_i,i\in \mathcal{I}$ are the Inequality Constraint.

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For example

\mathcal{E} &= Ø \\ \mathcal{I} &= \{1,2\} \end{align}