
Journal of Convex Analysis 19 (2012), No. 4, 10171032 Copyright Heldermann Verlag 2012 On Stability of Solutions to Systems of Convex Inequalities Alexander Ioffe Dept. of Mathematics, Technion  Israel Inst. of Technology, Haifa 32000, Israel ioffe@math.technion.ac.il [Abstractpdf] For systems of relations $\varphi_t(x)\le p_t,\; t\in T$, $Ax=y$, where $T$ is an arbitrary set, $\varphi_t$ is a convex l.s.c. function on a Banach space $X$ for every $t$ and $A$ is a linear bounded operator from $X$ into another Banach space $Y$, we discuss the following three problems:\\ (a) stability of solutions with respect to variations of the right hand side;\\ (b) effect of linear perturbations of functions $\varphi_t$ and mapping $A$;\\ (c) distance to infeasibility (the minimal norm of linear perturbations that make the system infeasible.) [ Fulltextpdf (169 KB)] for subscribers only. 