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√ √ √
Of a point-to-set map, let N [S]bea neigh- {x : g(x) ≤ b}= [− 2 − 1 + b, − 2 +
e
√
borhood of the set S. For each e> 0, there exists 1 + b]/[− log b, ∞), which is not bounded.
k
K such that for all k > K, A(x ) is a subset of The map fails to be (USC) at 0 due to the lack of
N [A(x)]. Here is an example of what can go
e stability of its feasibility region when perturbing
wrong. Consider the feasibility map with its right-hand side (from above).
√ 2
(x + 2) − 1if x< 0
upper triangular matrix A square matrix,
g(x) = A, such that A(i, j) = 0 for i ≥ j.
exp{−x} if x ≥ 0
Note g is continuous and its level set is utility function A measure of benefit, used
√ √
[− 2 − 1, − 2 + 1]. However, for any b> 0, as a maximand in economic models.
© 2003 by CRC Press LLC
© 2003 by CRC Press LLC
