We prove the existence of piecewise polynomials strictly convex smooth functions which converge uniformly on compact subsets to the Aleksandrov solution of the Monge-Ampère equation. We extend the Aleksandrov theory to right hand side only locally integrable and on convex bounded domains not necessarily strictly convex. The result suggests that for the numerical resolution of the equation, it i...

We study the radial-hedgehog solution on a three-dimensional (3D) spherical shell with radial boundary conditions, within the Landau-de Gennes theory for nematic liquid crystals. We prove that the radial-hedgehog solution is the unique minimizer of the Landaude Gennes energy in two separate regimes: (i) for thin shells when the temperature is below the critical nematic supercooling temperature ...

the problem of utilizing undesirable (bad) outputs in dea models often need replacing the assumption of free disposability of outputs by weak disposability of outputs. the kuosmanen technology is the only correct representation of the fully convex technology exhibiting weak disposability of bad and good outputs. also, there are some specific features of non-radial data envelopment analysis (dea...

We study the problem of finding a shortest tour visiting a given sequence of convex bodies in R. To our knowledge, this is the first attempt to attack the problem in its full generality: we investigate high-dimensional cases (d ≥ 2); we consider convex bodies bounded by (hyper)planes and/or (hyper)spheres; we do not restrict the start and the goal positions of the tour to be single points, we m...

• The DDL is decomposed by the hierarchical-clustering-oriented RBF framework at each time step. multi-dimensional interval model used to quantify convex-fuzzy hybrid uncertainties. fuzzy bounds of can be obtained based on Chebyshev-interval surrogate model. Load identification a hotly studied topic due widespread recognition its importance in structural design and health monitoring. This paper...

Solutions to optimization problems of convex type are typically characterized by saddle point conditions in which the primal vector is paired with a dual ‘multiplier’ vector. This paper investigates the behavior of such a primal-dual pair with respect to perturbations in parameters on which the problem depends. A necessary and sufficient condition in terms of certain matrices is developed for t...

INTRODUCTION Let F be a family of convex sets in R. A geometric transversal is an affine subspace that intersects every member of F . More specifically, for a given integer 0 ≤ k < d, a k-dimensional affine subspace that intersects every member of F is called a ktransversal to F . Typically, we are interested in necessary and sufficient conditions that guarantee the existence of a k-transversal...