Global Error Bounds for Convex Conic Problems

Shuzhong Zhang
2000 SIAM Journal on Optimization  
In this paper Lipschitzian type error bounds are derived for general convex conic problems under various regularity conditions. Speci cally, 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.
more » ... ality systems. Moreover, some of the results are also generalized to the intersection of multiple cones. Under Slater's condition alone, a global Lipschitzian type error bound may not hold. However, it is shown that such an error bound holds for a speci c region. For linear systems we show that the constant involved in Ho man's error bound can be estimated by the so-called condition number for linear programming.
doi:10.1137/s105262349834429x fatcat:kg6pfjnvlrbmxgzighitquqgny