In this paper we present an improved neural network to solve strictly convex quadratic programming(QP) problem. The proposed model is derived based on a piecewise equation correspond to optimality condition of convex (QP) problem and has a lower structure complexity respect to the other existing neural network model for solving such problems. In theoretical aspect, stability and global converge...

We prove an isoperimetric inequality for uniformly log-concave measures and for the uniform measure on a uniformly convex body. These inequalities imply the log-Sobolev inequalities proved by Bobkov and Ledoux [12] and Bobkov and Zegarlinski [13]. We also recover a concentration inequality for uniformly convex bodies, similar to that proved by Gromov and Milman [22].

In the paper we study closures of classes of log–concave measures under taking weak limits, linear transformations and tensor products. We consider what uniform measures on convex bodies can one obtain starting from some class K. In particular we prove that if one starts from one–dimensional log–concave measures, one obtains no non– trivial uniform mesures on convex bodies.

In this paper we give an optimal O(n log n) time and O(n) space algorithm to compute the rectilinear convex layers of a set S of n points on the plane. We also compute the rotation of S that minimizes the number of rectilinear convex layers in O(n log n) time and O(n) space.

This paper presents a dynamic algorithm for the construction of the Euclidean Voronoi diagram of a set of convex objects in the plane. We consider first the Voronoi diagram of smooth convex objects forming pseudocircles set. A pseudo-circles set is a set of bounded objects such that the boundaries of any two objects intersect at most twice. Our algorithm is a randomized dynamic algorithm. It do...

Let K, D be convex centrally symmetric bodies in R. Let k < n and let dk(K, D) be the smallest Banach–Mazur distance between k-dimensional sections of K and D. Define ∆(k, n) = sup dk(K, D), where the supremum is taken over all n−dimensional convex symmetric bodies K, D. We prove that for any k < n ∆(k, n) ∼log n {√ k if k ≤ n k2 n if k > n , where A ∼log n B means that 1/(C log n) ·A ≤ B ≤ (C ...

We introduce a new method of proving lower bounds on the depth of algebraic d-degree decision (resp. computation) trees and apply it to prove a lower bound ~2 (log N) (resp. f2 (log N/log log N)) for testing membership to an n-dimensional convex polyhedron having N faces of all dimensions, provided that N > ( n d ) ~( ' ) (resp. N > nU<n)). This bound apparently does not follow from the methods...

The Catalan-Larcombe-French sequence {Pn}n≥0 arises in a series expansion of the complete elliptic integral of the first kind. It has been proved that the sequence is log-balanced. In the paper, by exploring a criterion due to Chen and Xia for testing 2-log-convexity of a sequence satisfying three-term recurrence relation, we prove that the new sequence {P2 n – Pn–1Pn+1}n≥1 are strictly log-con...

If & ^ 1 for each v, then by reasoning analogous to that of the preceding example, it may be shown, for any set (a), that there is no point p such that tp implies that log St(a, £) is concave. Hence Theorem 4 applies to all such functions log St(a, £). However, for this case the conclusion of the general theorem is weaker than the...

We study data structures for providing ε-approximations of convex functions whose slopes are bounded from above and below by n and −n, respectively. The structures we describe have size O((1/ε) log n) and can answer queries in O(log(1/ε) + log log n) time. We also give an informationtheoretic lower-bound, that shows it is impossible to obtain structures of size O(1/ε) for approximating this cla...