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Journal of Convex Analysis 19 (2012), No. 4, 1017--1032
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


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.)

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