The constrained vector optimization problem [image omitted] is studied, where [image omitted], [image omitted] and [image omitted] are C1,1 functions, and [image omitted] and [image omitted] are closed convex cones. In terms of the second-order Dini set-valued directional derivative, second-order necessary conditions a point x0 to be a weakly efficient point and second-order sufficient conditions x0 to be an isolated minimizer of order two are established.
Second-order Dini set-valued directional derivative in $C^{1,1} vector optimization
IVANOV, IVAN GINCHEV;GUERRAGGIO, ANGELO;ROCCA, MATTEO
2010-01-01
Abstract
The constrained vector optimization problem [image omitted] is studied, where [image omitted], [image omitted] and [image omitted] are C1,1 functions, and [image omitted] and [image omitted] are closed convex cones. In terms of the second-order Dini set-valued directional derivative, second-order necessary conditions a point x0 to be a weakly efficient point and second-order sufficient conditions x0 to be an isolated minimizer of order two are established.
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