Sentence examples for be a differentiable convex from inspiring English sources

Let be a differentiable convex.

Let (f:(0,infty)rightarrowmathbb{R}) be a differentiable convex function with the property that (f(1)=0).

Theorem 2.1 Let a, b ∈ R with a < b and f : [ a, b ] → R be a differentiable convex function.

Let J be an interval such that g ( x ) ∈ J for every x ∈ [ a, b ] and f : J → R be a differentiable convex function.

Theorem 2.1 Let f : [ a, b ] → R be a differentiable convex function and g : [ a, b ] → [ 0, ∞ ] be a continuous function.

Let θ : H → R be a differentiable convex function such that θ' is a L-Lipschitz continuous and β-strongly monotone operator for some L > 0 and β > 0. Under these assumptions, there exists a unique point x ̃ † ∈ S b for b ∈ D A K † such that θ x ̃ † = min θ ( x ) : x ∈ S b. (3.18).

Suppose that (Y=[0,1]) and (H : Yrightarrow Y ) is a differentiable convex function with (H (0 )= 0).

Suppose that (Y=[0,1]) and (H : Yrightarrow Y ) is a differentiable convex function such that (H (0 )= 0) and (H ^{prime} y geq1 ) for all (y in Y).

Since H is a differentiable convex function, by Theorem 2.8 we have H (t )- H (y )geq H ^{prime} y) (t - y ) and by assumption (2), H (t )- H (y )geq(t - y ) for all (t in Y).

Assume that (H : Yrightarrow Y ) is a differentiable convex function and (circ,star: Y timesmu(Sigma rightarrow Y ) are non-decreasing operators satisfying the following conditions: 1. (a star0 = a circ0 = 0);   2.

Since the problem in Proposition 3.1 is a differentiable convex optimization problem with linear constraints, not only is the KKT condition mentioned above sufficient, but it is also necessary for optimality.