ArticleOriginal scientific text

Title

Equilibrium of maximal monotone operator in a given set

Authors 1

Affiliations

  1. Technical University of Łódź, ul. Żwirki 36, 90-924 Łódź, Poland

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].

Keywords

subdifferentials, maximal monotonicity, equilibrium points, min-max

Bibliography

  1. A. Drwalewska and L. Gajek, On Localizing Global Pareto Solutions in a Given Convex Set, Applicationes Mathematicae 26 (1999), 383-301.
  2. L. Gajek and D. Zagrodny, Countably Orderable Sets and Their Applications in Optimization, Optimization 26 (1992), 287-301.
  3. R.R. Phelps, Convex Functions, Monotone Operators and Differentiability, Springer-Verlag, Berlin, Heidelberg 1989.
  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.
  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.
  9. S. Simons, Swimming Below Icebergs, Set-Valued Analysis 2 (1994), 327-337.
  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.
Pages:
159-169
Main language of publication
English
Received
1999-11-06
Accepted
2000-04-05
Published
2000
Exact and natural sciences