Sentence examples for the epigraph of a function from inspiring English sources

The epigraph of a function,, is defined by (2.8).

The epigraph of a function g : R n → R ∪ , epig, is defined by epi g = { ( x, r ) ∈ R n × R ∣ g ( x ) ≦ r }.

Nonlinear optimization relies on the following definitions for functions: The graph of a function f is the set of the pairs of arguments x and function evaluations f(x) Graph(f) = { (x, f(x) ) } The epigraph of a real-valued function f is the set of points above the graph Epi(f) = { (x, u) : f(x) ≤ u }.

I came to know this passage by heart through re-reading, and borrowed it for the epigraph of a novel.

For the definitions of conjugate and epigraph of a function one can see Bector et al. [2].

By using the properties of the epigraph of the conjugate functions, the optimality conditions and strong duality of are obtained.

By using the properties of the epigraph of the conjugate functions, we give some new constraint qualifications, which characterizes completely the strong duality and the stable strong duality.

and the epigraph of is a set in : (2.4).

The epigraph of is a set in : (2.6).

The state constraint is the epigraph of the minimal solution of a second Hamilton Jacobi equation.

You have a quote in the epigraph of your book from John Kenneth Galbraith: "There's a certain part of the contented majority who love anybody worth a billion dollars".