List of Titles

Authors: Adly, Samir , Outrata, Jiri
Date: 2013
Type: Text , Journal article
Relation: Journal of Convex Analysis Vol. 20, no. 1 (2013), p. 43-66
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Description: The main concern of this paper is to investigate some stability properties (namely Aubin property and isolated cahnness) of a special non-monotone variational inclusion. We provide a characterization of these properties in terms of the problem data and show their importance for the design of electrical circuits involving nonsmooth and non-monotone electronic devices Uke DIAC (Diode Alternating Current). Circuits with other devices like SCR (Silicon Controlled Rectifiers), Zener diodes, thyristors, varactors and transistors can be analyzed in the same way. © Heldermann Verlag.
Description: 2003011029

Authors: Červinka, Michal , Outrata, Jiri , Pištěk, M
Date: 2014
Type: Text , Journal article
Relation: Set-Valued and Variational Analysis Vol. 22, no. 3 (2014), p. 575-595
Relation: http://purl.org/au-research/grants/arc/DP110102011
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Description: We consider parameterized Mathematical Programs with Complementarity Constraints arising, e.g., in modeling of deregulated electricity markets. Using the standard rules of the generalized differential calculus we analyze qualitative stability of solutions to the respective M-stationarity conditions. In particular, we provide characterizations and criteria for the isolated calmness and the Aubin properties of the stationarity map. To this end, we introduce the second-order limiting coderivative of mappings and provide formulas for this notion and for the graphical derivative of the limiting coderivative in the case of the normal cone mapping to ℝn Funding ARC- Australian Research Council

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On the Aubin property of solution maps to parameterized variational systems with implicit constraints

Authors: Gfrerer, Helmut , Outrata, Jiri
Date: 2020
Type: Text , Journal article
Relation: Optimization Vol. 69, no. 7-8 (2020), p. 1681-1701
Relation: http://purl.org/au-research/grants/arc/DP160100854
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Description: In the paper, a new sufficient condition for the Aubin property to a class of parameterized variational systems is derived. In these systems, the constraints depend both on the parameter as well as on the decision variable itself and they include, e.g. parameter-dependent quasi-variational inequalities and implicit complementarity problems. The result is based on a general condition ensuring the Aubin property of implicitly defined multifunctions which employs the recently introduced notion of the directional limiting coderivative. Our final condition can be verified, however, without an explicit computation of these coderivatives. The procedure is illustrated by an example. © 2019, © 2019 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group.
Description: The research of the first author was supported by the Austrian Science Fund (FWF) under grant P29190-N32. The research of the second author was supported by the Grant Agency of the Czech Republic, Project 17-04301S and the Australian Research Council, Project 10.13039/501100000923DP160100854.

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On the Aubin property of a class of parameterized variational systems

Authors: Gfrerer, Helmut , Outrata, Jiri
Date: 2017
Type: Text , Journal article
Relation: Mathematical Methods of Operations Research Vol. 86, no. 3 (2017), p. 443-467
Relation: http://purl.org/au-research/grants/arc/DP160100854
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Description: The paper deals with a new sharp condition ensuring the Aubin property of solution maps to a class of parameterized variational systems. This class encompasses various types of parameterized variational inequalities/generalized equations with fairly general constraint sets. The new condition requires computation of directional limiting coderivatives of the normal-cone mapping for the so-called critical directions. The respective formulas have the form of a second-order chain rule and extend the available calculus of directional limiting objects. The suggested procedure is illustrated by means of examples. © 2017, Springer-Verlag GmbH Germany.

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On lipschitzian properties of implicit multifunctions

Authors: Gfrerer, Helmut , Outrata, Jiri
Date: 2016
Type: Text , Journal article
Relation: SIAM Journal on Optimization Vol. 26, no. 4 (2016), p. 2160-2189
Relation: http://purl.org/au-research/grants/arc/DP160100854
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Description: This paper is devoted to the development of new sufficient conditions for the calmness and the Aubin property of implicit multifunctions. As the basic tool we employ the directional limiting coderivative which, together with the graphical derivative, enables a fine analysis of the local behavior of the investigated multifunction along relevant directions. For verification of the calmness property, in addition, a new condition has been discovered which parallels the missing implicit function paradigm and permits us to replace the original multifunction by a substantially simpler one. Moreover, as an auxiliary tool, a handy formula for the computation of the directional limiting coderivative of the normal-cone map with a polyhedral set has been derived which perfectly matches the framework of [A. L. Dontchev and R. T. Rockafellar, SIAM J. Optim., 6 (1996), pp. 1087{1105]. All important statements are illustrated by examples. © 2016 Society for Industrial and Applied Mathematics.

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Stability analysis for parameterized variational systems with implicit constraints

Authors: Benko, Matúš , Gfrerer, Helmut , Outrata, Jiri
Date: 2020
Type: Text , Journal article
Relation: Set-Valued and Variational Analysis Vol. 28, no. 1 (2020), p. 167-193
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Description: In the paper we provide new conditions ensuring the isolated calmness property and the Aubin property of parameterized variational systems with constraints depending, apart from the parameter, also on the solution itself. Such systems include, e.g., quasi-variational inequalities and implicit complementarity problems. Concerning the Aubin property, possible restrictions imposed on the parameter are also admitted. Throughout the paper, tools from the directional limiting generalized differential calculus are employed enabling us to impose only rather weak (non- restrictive) qualification conditions. Despite the very general problem setting, the resulting conditions are workable as documented by some academic examples. © 2019, The Author(s).

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