Sentence examples for be the convex function from inspiring English sources

Let be a real number and let be the convex function defined by.

Let (varphi _{lambda,gamma }:mathbb R rightarrow mathbb R ) be the convex function defined as begin{aligned} varphi _{lambda,gamma }(t)= t-lambda )^gamma _-= t-lambdagin{array}{ll} (lambda -t)^gamma, &quad tle lambda 0, &quad t>lambda.

where is the convex function.

where is the convex function given by,.

Equation (22) is the convex function of P s, and there is a unique optimal solution.

The Fenchel conjugate function of f is the convex function f ∗ : E → R defined by f ∗ = s u p { 〈 ξ, x 〉 - f ( x ) : x ∈ E }.

For this reason, (-t_{s}log _{2}big (1+ frac {p_{ss} gamma _{ss}}{t_{s}}big)) is the convex function of (p ss,t s ).

The Fenchel conjugate function of f is the convex function (f^: E rightarrow -infty,+infty)) defined by f^bigl(x^bigrightarrow -inftyangle x^,xbigrrangle -f(x), x in Ebigr}.

For modeling purposes a linear function is chosen that approaches the convex function in the interval of the expected number of optimal locations.

As the left-hand derivative of the convex function is nondecreasing function, we have (3.18).

An m-convex function need not be a convex function, as the following example shows.