Caption: Testing the convex
surfaces was done by looking at interference fringes with a matching concave surface of known quality.
In order to get the unique optimal solution we have used the convex
approach along with gradient based technique named as Lagrange multiplier which is one of the most constructive techniques for finding such maxima and minima.
Apart from the locally convex
topology [beta](X) on M(X), there are two other locally convex
structures on the space M(X) whose definitions are as follows.
Usually, denoising model is defined as one combination of a quadratic data fidelity term and a convex
regularization term or a differential regularization, for example, convex
but nonsmooth problem 
ii) For any fixed y [member of] K, u [member of] T(x), the mapping x [right arrow] <u, [eta](x, y)> is convex
This article is structured as follows: section two introduces the standard model and studies the equivalence of the games induced by a convex
and a concave transport cost function.
Note D is convex
and since (Dn) is increasing we have
n] [right arrow] R is a continuously differentiable convex
j] be two vertices of the convex
polygon that admit parallel lines of support, and have internal angles less than 180[degrees], as in the example of Fig.
They claim that their rules can be applied to develop other classes of convex
alpha]]t > 0 and [PHI] [member of] C((c,d), R) is convex
We will study a particular effect of geometry on the f-vector: if a polytope is close to a convex
body whose boundary is sufficiently smooth, then the shape of the g-vector, and hence also of the f-vector is subject to additional constraints stronger than the ones of the general g-theorem.