Abstract.In this paper we define a new condition number ?(A) for the following problem: given a m by n matrix A, find x∈ℝn, s.t. Ax<0. We characterize this condition number in terms of distance to… Expand

We define a condition number (A,b,c) for a linear program min x s.t. Ax=b,x≥0 and give two characterizations via distances to degeneracy and singularity.Expand

We prove that for a large class of problems, including those with a discrete set of inputs, their level-2 condition number (essentially) coincides with the original one.Expand

We define and characterize a condition number for the conic feasibility problem that exploits the possible factorization of $K$ as a product of simpler cones.Expand

In this paper, we provide bounds for the expected value of the log of the condition number C(A) of a linear feasibility problem given by a n × m matrix A (Ref. 1). We show that this expected value is… Expand

We describe an algorithm that first decides whether the primal-dual pair of linear programs min cTx max bTy s.t. is feasible and in case it is, computes an optimal basis and optimal solutions.Expand

This chapter describes the complexity theoretic properties of interior-point algorithms, a combinatorial optimization problem involving selecting an extreme point among a finite set of possible vertices.Expand

We develop upper and lower bounds on the decay rates of the distribution tails of $\mathscr C(A)$, showing that ${\bf P}\left[\mathsc R(A)\geq t\right]\sim c/t for large t, where c is a factor that depends only on the problem dimensions $(m,n)$.Expand

The set of ill-posed matrices for the problems (P) and (D) is the set of matrices A for which one of these problems is strictly feasible and remains so for arbitrarily small perturbations on A.Expand