Equilibrium of maximal monotone operator in a given set

Dariusz Zagrodny

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

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

Abstract

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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].

How to cite

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Dariusz 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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  1. [1] A. Drwalewska and L. Gajek, On Localizing Global Pareto Solutions in a Given Convex Set, Applicationes Mathematicae 26 (1999), 383-301. Zbl1010.90071
  2. [2] L. Gajek and D. Zagrodny, Countably Orderable Sets and Their Applications in Optimization, Optimization 26 (1992), 287-301. Zbl0815.49020
  3. [3] R.R. Phelps, Convex Functions, Monotone Operators and Differentiability, Springer-Verlag, Berlin, Heidelberg 1989. Zbl0658.46035
  4. [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. [5] M. Przeworski, Lokalizacja Punktów Wykresu Operatora Maksymalnie Monotonicznego, Praca doktorska, Instytut Matematyki Politechniki ódzkiej 1999. 
  6. [6] R.T. Rockafellar and R.J-B. Wets, Variational Analysis, Springer-Verlag, Berlin, Heidelberg 1998. Zbl0888.49001
  7. [7] S. Rolewicz, Metric Linear Spaces, PWN, Warszawa and D. Reidel Publishing Company, Dordrecht, Boston 1984. 
  8. [8] S. Simons, Subtangents with Controlled Slope, Nonlinear Analysis, Theory, Methods and Applications 22 (11) (1994), 1373-1389. Zbl0836.49009
  9. [9] S. Simons, Swimming Below Icebergs, Set-Valued Analysis 2 (1994), 327-337. Zbl0807.46002
  10. [10] S. Simons, Minimax and Monotonicity, Springer-Verlag, Berlin, Heidelberg 1998. 
  11. [11] E. Zeidler, Nonlinear Functional Analysis and Its Applications, IIB Nonlinear Monotone Operators, Springer-Verlag, Berlin, Heidelberg 1989. 
  12. [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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