A new polynomial-time algorithm for linear programming
Combinatorica
Toward probabilistic analysis of interior-point algorithms for linear programming
Mathematics of Operations Research
Stable Numerical Algorithms for Equilibrium Systems
SIAM Journal on Matrix Analysis and Applications
A primal-dual interior point method whose running time depends only on the constraint matrix
Mathematical Programming: Series A and B
Condition numbers for polyhedra with real number data
Operations Research Letters
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We present formulations of two condition measures (one for linear programming (LP) due to Ye, and the other for a matrix) as optimization problems over sign constraints. We construct, based on LP duality, a dual characterization of Ye's condition measure in the setting of Karmarkar's form. The elementary formulations (utilizing the dual characterization) lead to trivial proofs of some results relating these two condition measures for polyhedra in Karmarkar's form. Such interpretations, using the sign constraints, allow for the definition of families of condition measures that are ''between'' the two condition measures. Our viewpoint provides further understanding of the relationship of the two condition measures. As a result of this new understanding, we point to a connection with oriented matroids and prove that a conjecture of Vavasis and Ye on the relationship of these two condition measures is false.