Second order optimality conditions for differentiable multiobjective problems

Giancarlo Bigi; Marco Castellani

RAIRO - Operations Research (2010)

  • Volume: 34, Issue: 4, page 411-426
  • ISSN: 0399-0559

Abstract

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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.

How to cite

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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 -

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