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.
Bianchi, M., Miglierina, E., Molho, E., Pini, R., Some results on condition numbers in convex multiobjective optimization, <<Some results on condition numbers in convex multiobjective optimization>>, 2011; 2011 (119): 1-16 [http://hdl.handle.net/10807/28860]
Some results on condition numbers in convex multiobjective optimization
Bianchi, Monica;Miglierina, Enrico;Pini, Rita
2011
Abstract
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.
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