nction
<span class="math">\(g:(\mathbf{R}^n\times\mathbf{R}^m)\rightarrow(\mathbf{R}\cup-\infty)\)</span>,
the function</p>
<div class="math">
\[f:\mathbf{R}\rightarrow(\mathbf{R}\cup-\infty), \quad f(x) \triangleq \sup\left\{\,g(x,y)\,~|~\,\exists y,~(x,y)\in S \,\right\}\]</div>
<p>is concave. If <span class="math">\(g(x,y)\triangleq y\)</span>, then</p>
<div class="math">
\[f(x) \triangleq \sup\left\{\,y\,~|~\,\exists y,~(x,y)\in S\,\right\}\]</div>
<p>gives the <em>hypograph</em> representation of <span