Sentence examples for be a convex operator from inspiring English sources

Let be a convex operator.

It is clear that if is a sublinear operator, then must be a convex operator, but the converse is not true in general.

Then A is a convex operator.

So, (G(f)) is a convex operator.

The purpose of this paper is to study the convex composite optimization problem: min_{x in mathbb{R}^{l}} phi(x):= h bigl(F x) bigr), (2.1) where (h : mathbb{R}^{m} rightarrow mathbb{R}) is a convex operator, (F : mathbb{R}^{l} rightarrow mathbb{R}^{m}) is a Fréchet-differentiable operator and (m, l in mathbb{N}^{star}).

An operator is called a convex operator, if the domain of is a nonempty convex subset of and if for all and all real number (2.5).

Since a sublinear operator is also a convex operator, so from corollary 3.4, we have the following result.

An operator (A: C to X) is called a convex operator if Abigl(tx+ 1-t ybigr preceq tx+ 1-t ybigr preceqall (x,y in C), (xpreceq y) and (tin[0,1]).

Let be a hemicontinuous monotone operator, let be a convex subset, and let be a convex function and a given point.

Let (mathcal{C} subsetmathcal{A}(H)) be a convex set and (f:mathcal{C} rightarrowmathcal{A}(H)) be operator convex.

Let be replaced by a single-valued map in Corollary 3.3, then we have the following Hahn-Banach extension theorem in which a concave operator is dominated by a convex operator.