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...

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...

In Leture 18, we have talked about Linear Programming (LP). LP refers to the following problem. We are given an input of the following m constraints (inequalities):

Off-the-shelf linear programming (LP) solvers trade soundness for speed: for efficiency, the arithmetic is not exact rational arithmetic but floating-point arithmetic. As a side-effect the results come without any formal guarantee and cannot be directly used for deciding linear arithmetic. In this work we explain how to design a sound procedure for linear arithmetic built upon an inexact floati...

Helly’s theorem says that if every d + 1 elements of a given finite set of convex objects in IR have a common point, then there is a point common to all of the objects in the set. We define three new types of Helly theorems: discrete Helly theorems where the common point should belong to an a-priori given set, lexicographic Helly theorems where the common point should not be lexicographically g...

minimizing production costs for a certain amount of product is one of the main concerns for managers of agricultural and animal husbandry units. much of the cost of a unit of livestock (almost 75%) is related to methods of nutrition and ration. accordingly, using some methods to reduce costs, including methods of mathematical programming, is required. the linear programming model was used as th...

Until recently, the study of interior point methods has dominated algorithmic research in semidefinite programming (SDP). From a theoretical point of view, these interior point methods offer everything one can hope for; they apply to all SDP’s, exploit second order information and offer polynomial time complexity. Still for practical applications with many constraints k, the number of arithmeti...

This paper presents an algorithm for solving interval linear programming(ILP) problems. Interval inequality constraints and equality constraints are discussed separately. The aim of the paper is to show that (ILP) problems can be decomposed into two general linear programming(LP) by the monotonicity of (LP) problems , and we can gain the interval objective values. Finally, the proposed method h...

We discuss an approach for solving the Bilinear Matrix Inequality (BMI) based on its connections with certain problems defined over matrix cones. These problems are, among others, the cone generalization of the linear programming (LP) and the linear complementarity problem (LCP) (referred to as the Cone-LP and the Cone-LCP, respectively). Specifically, we show that solving a given BMI is equiva...