A new polynomial-time algorithm for linear programming
Combinatorica
Mathematical Programming: Series A and B
Combinatorial optimization: algorithms and complexity
Combinatorial optimization: algorithms and complexity
Probabilistic models for linear programming
Mathematics of Operations Research
On adaptive-step primal-dual interior-point algorithms for linear programming
Mathematics of Operations Research
Toward probabilistic analysis of interior-point algorithms for linear programming
Mathematics of Operations Research
Finding an interior point in the optimal face of linear programs
Mathematical Programming: Series A and B
Interior point algorithms: theory and analysis
Interior point algorithms: theory and analysis
Probabilistic Analysis of An Infeasible-Interior-Point Algorithm for Linear Programming
Mathematics of Operations Research
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We are interested in the average behavior of interior-point methods (IPMs) for linear programming problems (LPs). We use the rotation-symmetry-model as the probabilistic model for the average case analysis. This model had been used by Borgwardt in his average case analysis of the simplex-method. IPMs solve LPs in three phases. First, one has to find an appropriate starting point, then a sequence of interior points is generated, which converges to the optimal face. Finally, the optimum has to be calculated, as it is not an interior point. We present upper bounds on the average number of iterations in the first and the third phase by looking at random figures of the underlying polyhedron. These bounds show, that IPMs solve LPs in strongly polynomial time in the average case, so only the dimension parameters and not the encoding length of the problem determine the average behavior of IPMs.