Global Error Bounds for Systems of Convex Polynomials over Polyhedral Constraints

This paper is devoted to study the Lipschitzian/Holderian type global error bound for systems of many finitely convex polynomial inequalities over a polyhedral constraint. Firstly, for systems of this type, we show that under a suitable asymtotic qualification condition, the Lipschitzian type global error bound property is equivalent to the Abadie qualification condition, in particular, the Lipschitzian type global error bound is satisfied under the Slater condition. Secondly, without regularity conditions, the Hölderian global error bound with an implicit exponent is invertigated. Mathematics Subject Classification: 49J52, 49J53, 90C30.