Global Error Bounds for Convex Conic Problems

This paper aims at deriving and proving some Lipschitzian type error bounds for convex conic problems in a simple way First it is shown that if the recession directions satisfy Slater s condition then a global Lipschitzian type error bound holds Alternatively if the feasible region is bounded then the ordinary Slater condition guarantees a global Lipschitzian type error bound These can be considered as generalizations of previously known results for inequality systems which also follow from general results in and However the proofs in the current paper are considerably simpler Some of the results are generalized to the intersection of multiple shifted cones with di erent shifts Under Slater s condition alone a global Lipschitzian type error bound does not hold It is shown however that such an error bound holds for a speci c conic region For linear systems we establish that the sharp constant involved in Ho man s error bound is nothing but the condition number for linear programming as used by Vavasis and Ye in