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Erschienen in:
2006 | OriginalPaper | Buchkapitel
Second-Order Conditions in C 1,1 Vector Optimization with Inequality and Equality Constraints
verfasst von : Ivan Ginchev, Angelo Guerraggio, Matteo Rocca
Erschienen in: Recent Advances in Optimization
Verlag: Springer Berlin Heidelberg
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The present paper studies the following constrained vector optimization problem: min
C
f
(
x
),
g
(
x
) ∈ −
K
,
h
(
x
) = 0, where
f
: ℝ
n
→ ℝ
m
g
: ℝ
n
→ ℝ
p
are
C
1,1
functions,
h
: ℝ
n
→ ℝ
q
is
C
2
function, and
C
⊂ ℝ
m
and
K
⊂ ℝ
p
are closed convex cones with nonempty interiors. Two type of solutions are important for the consideration, namely
w
-minimizers (weakly efficient points) and
i
-minimizers (isolated minimizers). In terms of the second-order Dini directional derivative second-order necessary conditions a point
x
0
to be a
w
-minimizer and second-order sufficient conditions
x
0
to be an
i
-minimizes of order two are formulated and proved. The effectiveness of the obtained conditions is shown on examples.