The complexity of iterative algorithms in numerical analysis often depends on the condition number of the input (for example, conjugate gradient method). Similarly, condition numbers have been introduced in the context of linear and conic programming, and play a role in the complexity analysis of interior point methods (among other things). In this talk I will discuss geometric measures of condition for linear and conic programming and present results about the probability distribution of these condition numbers on random inputs. As a consequence we obtain average-case complexity results for algorithms solving the conic feasibility problem.
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