We estimate the number of violator spaces of given dimension d and number of constraints n. We show that the number of nondegenerate regular violator spaces is at most n d , and that the number of all violator spaces is at least of order exp(n). This is related to the question whether the class of optimization problems described by violator spaces (or LP-type problems) is more general than line...

Violator Spaces were introduced by J. Matoušek et al. in 2008 as generalization of Linear Programming problems. Convex geometries were invented by Edelman and Jamison in 1985 as proper combinatorial abstractions of convexity. Convex geometries are defined by antiexchange closure operators. We investigate an interrelations between violator spaces and closure spaces and show that violator spaces ...

the money creation by commercial banks, raises the question whether this phenomenon is defensible and vindicable from the perspective of economic values and goals in islam? opponents of bank money creation introduce it as an anti-stability, violator of ethics, unfair, violator of state power in exercising its right to publish money and stimulator of no priority social activities while defenders...

This paper introduces a new type of violator model that is based on Markov chains. It can be used as scenario AS IS or mathematical with quantitative estimates if additional information presented. Our aim this was to develop will allow restore missing data, using existing knowledge about violator. The results show presented for general cases cover the majority attacks and applied real-life scen...

Sharir and Welzl introduced an abstract framework for optimization problems, called LP-type problems or also generalized linear programming problems, which proved useful in algorithm design. We define a new, and as we believe, simpler and more natural framework: violator spaces, which constitute a proper generalization of LP-type problems. We show that Clarkson's randomized algorithms for low-d...

Sharir and Welzl introduced an abstract framework for optimization problems, called LP-type problems or also generalized linear programming problems, which proved useful in algorithm design. We define a new, and as we believe, simpler and more natural framework: violator spaces, which constitute a proper generalization of LP-type problems. We show that Clarkson's randomized algorithms for low-d...

Clarkson’s algorithm is a two-staged randomized algorithm for solving linear programs. This algorithm has been simplified and adapted to fit the framework of LP-type problems. In this framework we can tackle a number of non-linear problems such as computing the smallest enclosing ball of a set of points in R. In 2006, it has been shown that the algorithm in its original form works for violator ...