A new polynomial-time algorithm for linear programming
Combinatorica
Modified barrier functions (theory and methods)
Mathematical Programming: Series A and B
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
An Accelerated Interior Point Method Whose Running Time Depends Only on $A$
An Accelerated Interior Point Method Whose Running Time Depends Only on $A$
Probabilistic analysis of condition numbers for linear programming
Journal of Optimization Theory and Applications
Learning Real Polynomials with a Turing Machine
ALT '99 Proceedings of the 10th International Conference on Algorithmic Learning Theory
Solving linear programs with finite precision: II. algorithms
Journal of Complexity
A primal--dual symmetric relaxation for homogeneous conic systems
Journal of Complexity
Solving linear programs with finite precision: II. Algorithms
Journal of Complexity
On the condition numbers for polyhedra in Karmarkar's form
Operations Research Letters
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We consider the complexity of finding a feasible point inside a polyhedron specified by homogeneous linear constraints. A primal-dual interior point method is used. The running time of the interior point method can be bounded in terms of a condition number of the coefficient matrix A that has been proposed by Ye. We demonstrate that Ye's condition number is bounded in terms of another condition number for weighted least squares discovered by Stewart and Todd. Thus, the Stewart-Todd condition number, which is defined for real-number data, also bounds the complexity of finding a feasible point in a polyhedron.