Linear programming, complexity theory and elementary functional analysis
Mathematical Programming: Series A and B
On the complexity of linear programming under finite precision arithmetic
Mathematical Programming: Series A and B
Condition measures and properties of the central trajectory of a linear program
Mathematical Programming: Series A and B
Techniques for automatic tolerance control in linear programming
Communications of the ACM
Accuracy and Stability of Numerical Algorithms
Accuracy and Stability of Numerical Algorithms
A Primal-Dual Algorithm for Solving Polyhedral Conic Systems with a Finite-Precision Machine
SIAM Journal on Optimization
Unifying Condition Numbers for Linear Programming
Mathematics of Operations Research
Rounding Errors in Algebraic Processes
Rounding Errors in Algebraic Processes
Condition numbers for polyhedra with real number data
Operations Research Letters
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We describe an algorithm that first decides whether the primal-dual pair of linear programsminc^Txmaxb^Tys.t.Ax=bs.t.A^Ty==0is feasible and in case it is, computes an optimal basis and optimal solutions. Here, A@?R^m^x^n,b@?R^m,c@?R^n are given. Our algorithm works with finite precision arithmetic. Yet, this precision is variable and is adjusted during the algorithm. Both the finest precision required and the complexity of the algorithm depend on the dimensions n and m as well as on the condition K(A,b,c) introduced in D. Cheung and F. Cucker [Solving linear programs with finite precision: I. Condition numbers and random programs, Math. Program. 99 (2004) 175-196].