Geodesic
On Stability of Solutions to Systems of Convex Inequalities
Journal of convex analysis, Tome 19 (2012) no. 4, pp. 1017-1032.

Voir la notice de l'article provenant de la source Heldermann Verlag

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.) 
@article{JCA_2012_19_4_JCA_2012_19_4_a7,
     author = {A. Ioffe},
     title = {On {Stability} of {Solutions} to {Systems} of {Convex} {Inequalities}},
     journal = {Journal of convex analysis},
     pages = {1017--1032},
     publisher = {mathdoc},
     volume = {19},
     number = {4},
     year = {2012},
     url = {http://geodesic.mathdoc.fr/item/JCA_2012_19_4_JCA_2012_19_4_a7/}
}
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A. Ioffe. On Stability of Solutions to Systems of Convex Inequalities. Journal of convex analysis, Tome 19 (2012) no. 4, pp. 1017-1032. http://geodesic.mathdoc.fr/item/JCA_2012_19_4_JCA_2012_19_4_a7/