D. Cheung

Publications19
h-index8
Citations210
Highly Influential Citations16
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A new condition number for linear programming
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
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Unifying Condition Numbers for Linear Programming
TLDR
This work has been substantially funded by a grant from the Research Grants Council of the Hong Kong SAR (project number CityU 1085/02P). Expand
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Solving linear programs with finite precision: I. Condition numbers and random programs
TLDR
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
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A note on level-2 condition numbers
TLDR
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
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A Condition Number for Multifold Conic Systems
TLDR
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
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Probabilistic Analysis of Condition Numbers for Linear Programming
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
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Solving linear programs with finite precision: II. Algorithms
TLDR
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
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Linear Programming and Condition Numbers under the Real Number Computation Model
TLDR
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
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Tail Decay and Moment Estimates of a Condition Number for Random Linear Conic Systems
TLDR
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
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On strata of degenerate polyhedral cones I: Condition and distance to strata
TLDR
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
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