Correction to "Analysis of the Implicit Euler Time-Discretization of a Class of Descriptor-Variable Linear Cone Complementarity Systems", J. Convex Analysis 29/2 (2022) 481–517

Quang-Hung Pham; Bernard Brogliato

doi:10.68381/jca31050

Abstract

This note corrects a mistake in a recent paper of B. Brogliatio [Analysis of the implicit Euler time-discretization of a class of descriptor-variable linear cone complementarity systems, J. Convex Analysis 29/2 (2022) 481–517] concerning the characterization of the domain of an operator of the form

\Phi(t,\cdot):=(\partial \sigma_{\Gamma(t)}+D)^{-1}(\cdot)

,

D=D^{\top}

a constant positive semi-definite matrix,

\Gamma(t)

a nonempty closed convex set for each

t

,

\sigma_{\Gamma(t)}(\cdot)

its support function.

Author information

Contact details are reproduced from the original publication and may be historical.

Quang-Hung Pham

Université Grenoble Alpes, INRIA, CNRS, Grenoble INP, LJK, Grenoble, France

Bernard Brogliato

Université Grenoble Alpes, INRIA, CNRS, Grenoble INP, LJK, Grenoble, France

Keywords

Linear complementarity problem
sum of operators
maximal monotone operator

Mathematics Subject Classification

65K15, 94C60, 49J53, 34A09, 34A12, 34A60

References

D. S. Bernstein: Matrix Mathematics. Theory, Facts and Formulas, Princeton University Press, Princeton (2009).https://doi.org/10.1515/9781400833344 Google Scholar
H. Brézis, A. Haraux: Image d’une somme d’opérateurs monotones et applications, Israel J. Math. 23/2 (1976) 165–186.https://doi.org/10.1007/BF02756796 Google Scholar
B. Brogliato: Analysis of the implicit Euler time-discretization of a class of descriptor-variable linear cone complementarity systems, J. Convex Analysis 29/2 (2022) 481–517.https://doi.org/10.68381/jca29029 Google Scholar
B. Brogliato, D. Goeleven: Existence, uniqueness of solutions and stability of nonsmooth multivalued Lur’e dynamical systems, J. Convex Analysis 20/3 (2013) 881–900.https://doi.org/10.68381/jca20047 Google Scholar
M. K. Camlibel, L. Iannelli, A. Tanwani: Convergence of proximal solutions for evolution inclusions with time-dependent maximal monotone operators, Math. Programming A 194 (2022) 1017–1059.https://doi.org/10.1007/s10107-021-01666-7 Google Scholar
R. W. Cottle, J. S. Pang, R. E. Stone: The Linear Complementarity Problem, Computer Science and Scientific Computing Series, Academic Press, New York (1992).Google Scholar
R. T. Rockafellar, R. J.-B. Wets: Variational Analysis, 3rd printing, Springer, Berlin (2009).Google Scholar
A. Tanwani, B. Brogliato, C. Prieur: Well-posedness and output regulation for implicit time-varying evolution variational inequalities, SIAM J. Control Optimization 56/2 (2018) 751–781.https://doi.org/10.1137/16M1083657 Google Scholar

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Published by Heldermann Verlag, 2024. Rights now held by Banach Press LLC.

[1] D. S. Bernstein: Matrix Mathematics. Theory, Facts and Formulas, Princeton University Press, Princeton (2009).https://doi.org/10.1515/9781400833344 Google Scholar

[2] H. Brézis, A. Haraux: Image d’une somme d’opérateurs monotones et applications, Israel J. Math. 23/2 (1976) 165–186.https://doi.org/10.1007/BF02756796 Google Scholar

[3] B. Brogliato: Analysis of the implicit Euler time-discretization of a class of descriptor-variable linear cone complementarity systems, J. Convex Analysis 29/2 (2022) 481–517.https://doi.org/10.68381/jca29029 Google Scholar

[4] B. Brogliato, D. Goeleven: Existence, uniqueness of solutions and stability of nonsmooth multivalued Lur’e dynamical systems, J. Convex Analysis 20/3 (2013) 881–900.https://doi.org/10.68381/jca20047 Google Scholar

[5] M. K. Camlibel, L. Iannelli, A. Tanwani: Convergence of proximal solutions for evolution inclusions with time-dependent maximal monotone operators, Math. Programming A 194 (2022) 1017–1059.https://doi.org/10.1007/s10107-021-01666-7 Google Scholar

[6] R. W. Cottle, J. S. Pang, R. E. Stone: The Linear Complementarity Problem, Computer Science and Scientific Computing Series, Academic Press, New York (1992).Google Scholar

[7] R. T. Rockafellar, R. J.-B. Wets: Variational Analysis, 3rd printing, Springer, Berlin (2009).Google Scholar

[8] A. Tanwani, B. Brogliato, C. Prieur: Well-posedness and output regulation for implicit time-varying evolution variational inequalities, SIAM J. Control Optimization 56/2 (2018) 751–781.https://doi.org/10.1137/16M1083657 Google Scholar