Global Error Bounds for Linear Semi-infinite System over Polyhedral Constraints

This paper studies the Lipschitz / Hölder type global error bound for a linear semi-infinite systemover a polyhedral constraint. It is shown that the linear semi-infinite system admits aLipschitz type global error bound,which extends many existing results assuming a Slater condition on the recession functionor the boundedness of the feasible solution set. The Lipschitz type global error bound is also established under the data in the linear semi-infinite systemvarying in a bounded polyhedral set. Moreover, we discuss the relationship among the Hölder type global error boundand several notions of Hölder-type metric regularity for the linear semi-infinite systemunder a certain asymptotic condition or a assumption on boundedness of the feasible solution set. Mathematics Subject Classification (2000) 49K40 · 90C29 · 90C31