We treat in this paper Linear Programming (LP) problems with uncertain data. The focus is on uncertainty associated with hard constraints: those which must be satisfied, whatever is the actual realization of the data (within a prescribed uncertainty set). We suggest a modeling methodology whereas an uncertain LP is replaced by its Robust Counterpart (RC). We then develop the analytical and comp...

A robust linear binary classification problem will be considered. Robustness will be for data with interval uncertainty, i.e., data points are unknown but their mean and bounds on their components are known. Convex optimization formulation for the problem is derived and the method is applied to a genomic micro-array data. An extension for this framework will be developed for data with uncertain...

Let X be a normed linear space. We investigate properties of vector functions F : [a, b] → X of bounded convexity. In particular, we prove that such functions coincide with the delta-convex mappings admitting a Lipschitz control function, and that convexity K aF is equal to the variation of F ′ + on [a, b). As an application, we give a simple alternative proof of an unpublished result of the fi...

Closure spaces have been previously investigated by Paul Edelman and Robert Jami-son as \convex geometries". Consequently, a number of the results given here duplicate theirs. However, we employ a slightly diierent, but equivalent, deening axiom which gives a new avor to our presentation. The major contribution is the deenition of a partial order on all subsets, not just closed (or convex) subs...

The tropical convex hull of a finite set of points in tropical projective space has a natural structure of a cellular free resolution. Therefore, methods from computational commutative algebra can be used to compute tropical convex hulls. This approach is computationally competitive with combinatorial methods. Tropical cyclic polytopes are also presented.

Let K be a smooth convex set. The convex hull of independent random points in K is a random polytope. Central limit theorems for the volume and the number of i dimensional faces of random polytopes are proved as the number of random points tends to infinity. One essential step is to determine the precise asymptotic order of the occurring variances.

We introduce a novel representation of classifier conditions based on convex hulls. A classifier condition is represented by a sets of points in the problem space. These points identify a convex hull that delineates a convex region of the problem space. The condition matches all the problem instances inside such region. We apply XCSF with convex conditions to function approximation problems and...

The Q-convexity is a kind of convexity in the discrete plane. This notion has practically the same properties as the usual convexity: an intersection of two Qconvex sets is Q-convex, and the salient points can be defined like the extremal points. Moreover a Q-convex set is characterized by its salient point. The salient points can be generalized to any finite subset of Z2.

K. S. Lau had shown that a reflexive Banach space has the Mazur Intersection Property (MIP) if and only if every closed bounded convex set is the closed convex hull of its farthest points. In this work, we show that in general this latter property is equivalent to a property stronger than the MIP. As corollaries, we recapture the result of Lau and characterize the w*-MIP in dual of RNP spaces.

In the present investigation, we obtain certain sufficient conditions for a normalized analytic function f(z) defined by the Dziok–Srivastava linear operator Hm1⁄2a1 to satisfy the certain subordination. Our results extend corresponding previously known results on starlikeness, convexity, and close to convexity. 2006 Elsevier Inc. All rights reserved.