Convexity preserving mappings in subbase convexity theory

Moreau’s Proximal Mappings and Convexity in Hamilton-jacobi Theory

Proximal mappings, which generalize projection mappings, were introduced by Moreau and shown to be valuable in understanding the subgradient properties of convex functions. Proximal mappings subsequently turned out to be important also in numerical methods of optimization and the solution of nonlinear partial differential equations and variational inequalities. Here it is shown that, when a con...

Convexity - Preserving Scattered Data Interpolation 33 2 . 3 Convexity Conditions

This study deals with constructing a convexity-preserving bivariate C interpolants to scattered data whenever the original data are convex. Sufficient conditions on lower bound of Bézier points are derived in order to ensure that surfaces comprising cubic Bézier triangular patches are always convex and satisfy C continuity conditions. Initial gradients at the data sites are estimated and then m...

Convexity preserving splines over triangulations

A general method is given for constructing sets of sufficient linear conditions that ensure convexity of a polynomial in Bernstein–Bézier form on a triangle. Using the linear conditions, computational methods based on macro-element spline spaces are developed to construct convexity preserving splines over triangulations that interpolate or approximate given scattered data.

Near convexity, metric convexity, and convexity

It is shown that a subset of a uniformly convex normed space is nearly convex if and only if its closure is convex. Also, a normed space satisfying a mild completeness property is strictly convex if and only if every metrically convex subset is convex. 1 Classical and constructive mathematics The arguments in this paper conform to constructive mathematics in the sense of Errett Bishop. This mea...

DEA with efficiency classification preserving conditional convexity