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second order necessary optimality conditions

RAIRO - Operations Research (1)

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Second order optimality conditions for differentiable multiobjective problems
Giancarlo Bigi, Marco Castellani
Journal:

RAIRO - Operations Research / Volume 34 / Issue 4 / October 2000

Published online by Cambridge University Press:

15 August 2002, pp. 411-426

Print publication:

October 2000
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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.