Search results for "convexity"
showing 10 items of 57 documents
On the exhaustive generation of k-convex polyominoes
2017
The degree of convexity of a convex polyomino P is the smallest integer k such that any two cells of P can be joined by a monotone path inside P with at most k changes of direction. In this paper we present a simple algorithm for computing the degree of convexity of a convex polyomino and we show how it can be used to design an algorithm that generates, given an integer k, all k-convex polyominoes of area n in constant amortized time, using space O(n). Furthermore, by applying few changes, we are able to generate all convex polyominoes whose degree of convexity is exactly k.
Vector-valued Hardy inequalities and B-convexity
2000
Inequalities of the form $$\sum\nolimits_{k = 0}^\infty {|\hat f(m_k )|/(k + 1) \leqslant C||f||_1 } $$ for allf∈H 1, where {m k } are special subsequences of natural numbers, are investigated in the vector-valued setting. It is proved that Hardy's inequality and the generalized Hardy inequality are equivalent for vector valued Hardy spaces defined in terms ff atoms and that they actually characterizeB-convexity. It is also shown that for 1<q<∞ and 0<α<∞ the spaceX=H(1,q,γa) consisting of analytic functions on the unit disc such that $$\int_0^1 {(1 - r)^{q\alpha - 1} M_1^q (f,r) dr< \infty } $$ satisfies the previous inequality for vector valued functions inH 1 (X), defined as the space ofX…
A general framework for a class of non-linear approximations with applications to image restoration
2018
Este artículo se encuentra disponible en la página web de la revista en la siguiente URL: https://www.sciencedirect.com/science/article/abs/pii/S0377042717301188 Este es el pre-print del siguiente artículo: Candela, V., Falcó, A. & Romero, PD. (2018). A general framework for a class of non-linear approximations with applications to image restoration. Journal of Computational and Applied Mathematics, vol. 330 (mar.), pp. 982-994, que se ha publicado de forma definitiva en https://doi.org/10.1016/j.cam.2017.03.008 This is the pre-peer reviewed version of the following article: Candela, V., Falcó, A. & Romero, PD. (2018). A general framework for a class of non-linear approximations with applic…
Tangent and Normal Cones in Nonconvex Multiobjective Optimization
2000
Trade-off information is important in multiobjective optimization. It describes the relationships of changes in objective function values. For example, in interactive methods we need information about the local behavior of solutions when looking for improved search directions.
Error bounds for a convexity-preserving interpolation and its limit function
2008
AbstractError bounds between a nonlinear interpolation and the limit function of its associated subdivision scheme are estimated. The bounds can be evaluated without recursive subdivision. We show that this interpolation is convexity preserving, as its associated subdivision scheme. Finally, some numerical experiments are presented.
ε-Regularized two-level optimization problems: Approximation and existence results
2006
The purpose of this work is to improve some results given in [12], relating to approximate solutions for two-level optimization problems. By considering an e-regularized problem, we get new properties, under convexity assumptions in the lower level problems. In particular, we prove existence results for the solutions to the e-regularized problem, whereas the initial two-level optimization problem may fail to have a solution. Finally, as an example, we consider an approximation method with interior penalty functions.
Counting common perpendicular arcs in negative curvature
2013
Let $D^-$ and $D^+$ be properly immersed closed locally convex subsets of a Riemannian manifold with pinched negative sectional curvature. Using mixing properties of the geodesic flow, we give an asymptotic formula as $t\to+\infty$ for the number of common perpendiculars of length at most $t$ from $D^-$ to $D^+$, counted with multiplicities, and we prove the equidistribution in the outer and inner unit normal bundles of $D^-$ and $D^+$ of the tangent vectors at the endpoints of the common perpendiculars. When the manifold is compact with exponential decay of correlations or arithmetic with finite volume, we give an error term for the asymptotic. As an application, we give an asymptotic form…
Non-preserved curvature conditions under constrained mean curvature flows
2014
We provide explicit examples which show that mean convexity (i.e. positivity of the mean curvature) and positivity of the scalar curvature are non-preserved curvature conditions for hypersurfaces of the Euclidean space evolving under either the volume- or the area preserving mean curvature flow. The relevance of our examples is that they disprove some statements of the previous literature, overshadow a widespread folklore conjecture about the behaviour of these flows and bring out the discouraging news that a traditional singularity analysis is not possible for constrained versions of the mean curvature flow.
Interpolated measures with bounded density in metric spaces satisfying the curvature-dimension conditions of Sturm
2011
We construct geodesics in the Wasserstein space of probability measure along which all the measures have an upper bound on their density that is determined by the densities of the endpoints of the geodesic. Using these geodesics we show that a local Poincar\'e inequality and the measure contraction property follow from the Ricci curvature bounds defined by Sturm. We also show for a large class of convex functionals that a local Poincar\'e inequality is implied by the weak displacement convexity of the functional.
Noncoincidence of Approximate and Limiting Subdifferentials of Integral Functionals
2011
For a locally Lipschitz integral functional $I_f$ on $L^1(T,\mathbf{R}^n)$ associated with a measurable integrand f, the limiting subdifferential and the approximate subdifferential never coincide at a point $x_0$ where $f(t,\cdot)$ is not subdifferentially regular at $x_0(t)$ for a.e. $t\in T$. The coincidence of both subdifferentials occurs on a dense set of $L^1(T,\mathbf{R}^n)$ if and only if $f(t,\cdot)$ is convex for a.e. $t\in T$. Our results allow us to characterize Aubin's Lipschitz-like property as well as the convexity of multivalued mappings between $L^1$-spaces. New necessary optimality conditions for some Bolza problems are also obtained.