TY - UNPB

T1 - Some results on condition numbers in convex multiobjective optimization

AU - Bianchi, Monica

AU - Miglierina, Enrico

AU - Pini, Rita

AU - Molho, Elena

PY - 2011

Y1 - 2011

N2 - Abstract Various notions of condition numbers are used to study some sensitivity aspects of scalar optimization problems. The aim of this paper is to introduce a notion of condition number to treat the case of a multiobjective optimization problem defined via m convex C^{1,1} objective functions on a given closed ball in \mathbb{R}^{n}.
Two approaches are proposed: the first one adopts a local point of view around a solution point, whereas the second one considers the solution set as a whole. We underline that, in the scalar case, both of them reduce to the condition number proposed by Zolezzi. Extensions of the Eckart--Young distance theorem are proved in both cases.

AB - Abstract Various notions of condition numbers are used to study some sensitivity aspects of scalar optimization problems. The aim of this paper is to introduce a notion of condition number to treat the case of a multiobjective optimization problem defined via m convex C^{1,1} objective functions on a given closed ball in \mathbb{R}^{n}.
Two approaches are proposed: the first one adopts a local point of view around a solution point, whereas the second one considers the solution set as a whole. We underline that, in the scalar case, both of them reduce to the condition number proposed by Zolezzi. Extensions of the Eckart--Young distance theorem are proved in both cases.

KW - Condition Number

KW - Eckart-Young theorem

KW - sensitivity in multiobjective optimization

KW - Condition Number

KW - Eckart-Young theorem

KW - sensitivity in multiobjective optimization

UR - http://hdl.handle.net/10807/28860

M3 - Working paper

BT - Some results on condition numbers in convex multiobjective optimization

ER -