Bigi, Giancarlo, and Castellani, Marco. "Second order optimality conditions for differentiable multiobjective problems." RAIRO - Operations Research 34.4 (2010): 411-426. <http://eudml.org/doc/116586>.
@article{Bigi2010,
abstract = {
A second order optimality condition for multiobjective optimization with a set constraint is
developed; this condition is expressed as the impossibility of nonhomogeneous linear systems.
When the constraint is given in terms of inequalities and equalities, it can be turned into
a John type multipliers rule, using a nonhomogeneous Motzkin Theorem of the Alternative. Adding weak
second order regularity assumptions, Karush, Kuhn-Tucker type conditions are therefore deduced.
},
author = {Bigi, Giancarlo, Castellani, Marco},
journal = {RAIRO - Operations Research},
keywords = {Second order necessary optimality conditions; descent directions;
second order contingent set; Abadie and Guignard type conditions.},
language = {eng},
month = {3},
number = {4},
pages = {411-426},
publisher = {EDP Sciences},
title = {Second order optimality conditions for differentiable multiobjective problems},
url = {http://eudml.org/doc/116586},
volume = {34},
year = {2010},
}
TY - JOUR
AU - Bigi, Giancarlo
AU - Castellani, Marco
TI - Second order optimality conditions for differentiable multiobjective problems
JO - RAIRO - Operations Research
DA - 2010/3//
PB - EDP Sciences
VL - 34
IS - 4
SP - 411
EP - 426
AB -
A second order optimality condition for multiobjective optimization with a set constraint is
developed; this condition is expressed as the impossibility of nonhomogeneous linear systems.
When the constraint is given in terms of inequalities and equalities, it can be turned into
a John type multipliers rule, using a nonhomogeneous Motzkin Theorem of the Alternative. Adding weak
second order regularity assumptions, Karush, Kuhn-Tucker type conditions are therefore deduced.
LA - eng
KW - Second order necessary optimality conditions; descent directions;
second order contingent set; Abadie and Guignard type conditions.
UR - http://eudml.org/doc/116586
ER -
