# Equilibrium of maximal monotone operator in a given set

Discussiones Mathematicae, Differential Inclusions, Control and Optimization (2000)

- Volume: 20, Issue: 2, page 159-169
- ISSN: 1509-9407

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topDariusz Zagrodny. "Equilibrium of maximal monotone operator in a given set." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 20.2 (2000): 159-169. <http://eudml.org/doc/271461>.

@article{DariuszZagrodny2000,

abstract = {Sufficient conditions for an equilibrium of maximal monotone operator to be in a given set are provided. This partially answers to a question posed in [10].},

author = {Dariusz Zagrodny},

journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},

keywords = {subdifferentials; maximal monotonicity; equilibrium points; min-max; maximal monotone operator; equilibrium point; lower semi-continuous convex function; subdifferential; maximal monotone set-valued mapping},

language = {eng},

number = {2},

pages = {159-169},

title = {Equilibrium of maximal monotone operator in a given set},

url = {http://eudml.org/doc/271461},

volume = {20},

year = {2000},

}

TY - JOUR

AU - Dariusz Zagrodny

TI - Equilibrium of maximal monotone operator in a given set

JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization

PY - 2000

VL - 20

IS - 2

SP - 159

EP - 169

AB - Sufficient conditions for an equilibrium of maximal monotone operator to be in a given set are provided. This partially answers to a question posed in [10].

LA - eng

KW - subdifferentials; maximal monotonicity; equilibrium points; min-max; maximal monotone operator; equilibrium point; lower semi-continuous convex function; subdifferential; maximal monotone set-valued mapping

UR - http://eudml.org/doc/271461

ER -

## References

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- [2] L. Gajek and D. Zagrodny, Countably Orderable Sets and Their Applications in Optimization, Optimization 26 (1992), 287-301. Zbl0815.49020
- [3] R.R. Phelps, Convex Functions, Monotone Operators and Differentiability, Springer-Verlag, Berlin, Heidelberg 1989. Zbl0658.46035
- [4] M. Przeworski and D. Zagrodny, Constrained Equilibrium Point of Maximal Monotone Operator via Variational Inequality, Journal of Applied Analysis 5 (1999), 147-152.
- [5] M. Przeworski, Lokalizacja Punktów Wykresu Operatora Maksymalnie Monotonicznego, Praca doktorska, Instytut Matematyki Politechniki ódzkiej 1999.
- [6] R.T. Rockafellar and R.J-B. Wets, Variational Analysis, Springer-Verlag, Berlin, Heidelberg 1998. Zbl0888.49001
- [7] S. Rolewicz, Metric Linear Spaces, PWN, Warszawa and D. Reidel Publishing Company, Dordrecht, Boston 1984.
- [8] S. Simons, Subtangents with Controlled Slope, Nonlinear Analysis, Theory, Methods and Applications 22 (11) (1994), 1373-1389. Zbl0836.49009
- [9] S. Simons, Swimming Below Icebergs, Set-Valued Analysis 2 (1994), 327-337. Zbl0807.46002
- [10] S. Simons, Minimax and Monotonicity, Springer-Verlag, Berlin, Heidelberg 1998.
- [11] E. Zeidler, Nonlinear Functional Analysis and Its Applications, IIB Nonlinear Monotone Operators, Springer-Verlag, Berlin, Heidelberg 1989.
- [12] D. Zagrodny, The Maximal Monotonicity of the Subdifferentials of Convex Functions: Simons' Problem, Set-Valued Analysis 4 (1996), 301-314. Zbl0867.49015

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