科研成果详情

In this paper we study the distribution of script C sign (A) and log script C sign (A), where script C sign (A) is a condition number for the linear conic system Ax ≤ 0, x ≠ 0, with A ∈ ℝ. For Gaussian matrices A we develop both upper and lower bounds on the decay rates of the distribution tails of script C sign (A), showing that P [script C sign (A) ≥ t] ∼ c/t for large t, where c is a factor that depends only on the problem dimensions (m, n). Using these bounds, we derive moment estimates for script C sign (A) and log script C sign (A) and prove various limit theorems for the cases where m and/or n are large. Combined with condition number based complexity analyses, our results yield tail information on the distribution of running times for interior-point or relaxation methods designed to solve the feasibility problem Ax ≤ 0, x ≠ 0. © 2005 Society for Industrial and Applied Mathematics.