Error bounds : Necessary and sufficient conditions
- Authors: Fabian, Marian , Henrion, René , Kruger, Alexander , Outrata, Jiri
- Date: 2010
- Type: Text , Journal article
- Relation: Set-Valued and Variational Analysis Vol. 18, no. 2 (2010), p. 121-149
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- Description: The paper presents a general classification scheme of necessary and sufficient criteria for the error bound property incorporating the existing conditions. Several derivative-like objects both from the primal as well as from the dual space are used to characterize the error bound property of extended-real-valued functions on a Banach space. © 2010 Springer Science+Business Media B.V.
Boris Mordukhovich, the never tiring traveller, celebrates his sixtieth birthday
- Authors: Henrion, René , Kruger, Alexander , Outrata, Jiri
- Date: 2008
- Type: Text , Journal article
- Relation: Set-Valued Analysis Vol. 16, no. 2-3 (2008), p. 125-127
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Some remarks on stability of generalized equations
- Authors: Henrion, René , Kruger, Alexander , Outrata, Jiri
- Date: 2012
- Type: Text , Journal article
- Relation: Journal of Optimization Theory and Applications Vol. 159, no. 3 (2012), p. 681-697
- Relation: http://purl.org/au-research/grants/arc/DP110102011
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- Description: The paper concerns the computation of the graphical derivative and the regular (Fréchet) coderivative of the solution map to a class of generalized equations, where the multivalued term amounts to the regular normal cone to a (possibly nonconvex) set given by C 2 inequalities. Instead of the linear independence qualification condition, standardly used in this context, one assumes a combination of the Mangasarian-Fromovitz and the constant rank qualification conditions. Based on the obtained generalized derivatives, new optimality conditions for a class of mathematical programs with equilibrium constraints are derived, and a workable characterization of the isolated calmness of the considered solution map is provided. © 2012 Springer Science+Business Media, LLC.
About errors bounds in metric spaces
- Authors: Fabian, Marian , Henrion, René , Kruger, Alexander , Outrata, Jiri
- Date: 2011
- Type: Text , Conference paper
- Relation: International Conference Operations Research p. 33-38
- Relation: http://purl.org/au-research/grants/arc/DP110102011
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- Description: The paper presents a general primal space classification scheme of necessary and suffficient criteria for the error bound property incorporating the existing conditions. Several primal space derivative-like objects - slopes are used to characterize the error bound property of extended-real valued functions on metric sapces.
On regular coderivatives in parametric equilibria with non-unique multipliers
- Authors: Henrion, René , Outrata, Jiri , Surowiec, Thomas
- Date: 2012
- Type: Text , Journal article
- Relation: Mathematical Programming Vol. 136, no. 1 (December 2012), p. 111-131
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- Description: This paper deals with the computation of regular coderivatives of solution maps associated with a frequently arising class of generalized equations (GEs). The constraint sets are given by (not necessarily convex) inequalities, and we do not assume linear independence of gradients to active constraints. The achieved results enable us to state several versions of sharp necessary optimality conditions in optimization problems with equilibria governed by such GEs. The advantages are illustrated by means of examples.
- Description: C1
Indexation strategies and calmness constants for uncertain linear inequality systems
- Authors: Cánovas, Maria , Henrion, René , López, Marco , Parra, Juan
- Date: 2018
- Type: Text , Book chapter
- Relation: The Mathematics of the Uncertain (part of the Studies in Systems, Decision and Control series) p. 831-843
- Relation: http://purl.org/au-research/grants/arc/DP160100854
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- Description: The present paper deals with uncertain linear inequality systems viewed as nonempty closed coefficient sets in the (n+ 1) -dimensional Euclidean space. The perturbation size of these uncertainty sets is measured by the (extended) Hausdorff distance. We focus on calmness constants—and their associated neighborhoods—for the feasible set mapping at a given point of its graph. To this aim, the paper introduces an appropriate indexation function which allows us to provide our aimed calmness constants through their counterparts in the setting of linear inequality systems with a fixed index set, where a wide background exists in the literature.