caa a22 4500 475769740 CHVBK 20180406123616.0 cr unu---uuuuu 170329e20000801xx s 000 0 eng 10.1007/s101070050016 doi (NATIONALLICENCE)springer-10.1007/s101070050016 Gugat Martin University of Trier, Department of Mathematics, 54286 Trier, Germany, e-mail: gugat@uni-trier.de, DE aut Error bounds for infinite systems of convex inequalities without Slater's condition [Elektronische Daten] [Martin Gugat] The feasible set of a convex semi-infinite program is described by a possibly infinite system of convex inequality constraints. We want to obtain an upper bound for the distance of a given point from this set in terms of a constant multiplied by the value of the maximally violated constraint function in this point. Apart from this Lipschitz case we also consider error bounds of Hölder type, where the value of the residual of the constraints is raised to a certain power.¶We give sufficient conditions for the validity of such bounds. Our conditions do not require that the Slater condition is valid. For the definition of our conditions, we consider the projections on enlarged sets corresponding to relaxed constraints. We present a condition in terms of projection multipliers, a condition in terms of Slater points and a condition in terms of descent directions. For the Lipschitz case, we give five equivalent characterizations of the validity of a global error bound.¶We extend previous results in two directions: First, we consider infinite systems of inequalities instead of finite systems. The second point is that we do not assume that the Slater condition holds which has been required in almost all earlier papers. Springer-Verlag Berlin Heidelberg, 2000 error bounds nationallicence Hölder error bound nationallicence semi-infinite program nationallicence convex inequalities nationallicence dual solutions nationallicence projection multipliers nationallicence weak Slater condition nationallicence Mangasarian-Fromovitz condition Mathematics Subject Classification (1991) nationallicence 20E28 nationallicence 20G40 nationallicence 20C20 nationallicence Mathematical Programming Springer-Verlag 88/2(2000-08-01), 255-275 0025-5610 88:2<255 2000 88 10107 https://doi.org/10.1007/s101070050016 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s101070050016 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Gugat Martin University of Trier, Department of Mathematics, 54286 Trier, Germany, e-mail: gugat@uni-trier.de, DE aut NATIONALLICENCE 773 0- Mathematical Programming Springer-Verlag 88/2(2000-08-01), 255-275 0025-5610 88:2<255 2000 88 10107 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer