DOI: 10.68381/jca19054 ISSN: 0944-6532
On Stability of Solutions to Systems of Convex Inequalities
Alexander Ioffe
For systems of relations
\varphi_t(x)\le p_t,\; t\in T
φ
t
(
x
)
≤
p
t
,
t
∈
T
,
Ax=y
A
x
=
y
, where
T
T
is an arbitrary set,
\varphi_t
φ
t
is a convex l.s.c. function on a Banach space
X
X
for every
t
t
and
A
A
is a linear bounded operator from
X
X
into another Banach space
Y
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
φ
t
and mapping
A
A
; (c) distance to infeasibility (the minimal norm of linear perturbations that make the system infeasible.)