Abstract. Let K be a closed bounded convex subset of Rn ; then by a result of the first author, which extends a classical theorem of Whitney there is a constantwm(K ) so that for every continuous function f on K there is a polynomial φ of degree at most m − 1 so that | f (x)− φ(x)| ≤ wm(K ) sup x,x+mh∈K |1h ( f ; x)|. The aim of this paper is to study the constant wm(K ) in terms of the dimensi...

This paper is dedicated to Giorgio Picci on the occasion of his 65th birthday. I have come to appreciate Giorgio not only as a great friend but also as a great scholar. When we first met at Brown University in 1973, he introduced me to his seminal paper [29] on splitting subspaces, which became the impetus for our joint work on the geometric theory of linear stochastic systems [23–26]. This led...

Visibility methods are often based on the existence of large convex occluders. We present an algorithm that for a given simple non-convex polygon P finds an approximate inner-cover by large convex polygons. The algorithm is based on an initial partitioning of P into a set C of disjoint convex polygons which are an exact tessellation of P . The algorithm then builds a set of large convex polygon...

We introduce the q-paranorm, investigate some of its properties. We further give an algorithm which constructs the best linear approximations under the q-paranorm.

We propose a convex, lower semi-continuous, coercive approximation of Euler’s elastica energy for images, which is thus very well-suited as a regularizer in image processing. The approximation is not quite the convex relaxation, and we discuss its close relation to the exact convex relaxation as well as the difficulties associated with computing the latter. Interestingly, the convex relaxation ...

We use the merit function technique to formulate a linearly constrained bilevel convex quadratic problem as a convex program with an additional convex-d.c. constraint. To solve the latter problem we approximate it by convex programs with an additional convex-concave constraint using an adaptive simplicial subdivision. This approximation leads to a branch-and-bound algorithm for finding a global...

We consider the following basic geometric problem: Given ∈ (0, 1/2), a 2-dimensional figure that consists of a black object and a white background is -far from convex if it differs in at least an fraction of the area from every figure where the black object is convex. How many uniform and independent samples from a figure that is -far from convex are needed to detect a violation of convexity wi...