Wednesday, 15:45 - 16:10 h, Room: H 2035


Amos Uderzo
On some calmness conditions for nonsmooth constraint systems


In various contexts of mathematical programming, constraints
appearing in optimization problems, which depend on parameters,
can be formalized as follows
f(p,x) ∈ C,
where f:P× X → Y and C ⊂ Y are given
problem data, and p plays the role of a parameter.
Useful insights on the problem
behaviour (stability and sensitivity) can be achieved
by a proper analysis of the corresponding feasible set
mapping, i.e. S:P → 2X
S(p)={x ∈ X: f(p,x) ∈ C}.
In this vein, whenever P and X have a metric space structure,
a property of S playing a crucial role, both from the
theoretical and the computational viewpoint, is calmness.
Mapping S is said to be calm at (p0,x0) if
x0 ∈ S(p0) and there exist r,, \zeta>0 and
l ≥ 0 such that

S(p)∩ B(x0,r) ⊆ B(S(p0),l d(p,p0)), ∀ p ∈ B(p0,\zeta),

where B(A,r)={x ∈ X:  ∈ fa ∈ Ad(x,a) ≤ r}.
This talk is devoted to the analysis of conditions for the calmness
of S. Such task is carried out by referring to recent developments
of variational analysis. Emphasis is given to the case in
which mapping f defining S is nonsmooth.


Talk 2 of the invited session Wed.3.H 2035
"Nonsmooth analysis with applications in engineering" [...]
Cluster 24
"Variational analysis" [...]


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