Equilibrium of maximal monotone operator in a given set

• Autorzy: Dariusz Zagrodny
• Języki publikacji: EN

Abstrakty

EN

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].

Słowa kluczowe

EN

subdifferentials; maximal monotonicity; equilibrium points; min-max

Kategorie tematyczne

• 47H05: Monotone operators and generalizations
• 49J52: Nonsmooth analysis

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae, Differential Inclusions, Control and Optimization
• Rocznik: 2000
• Tom: 20
• Numer: 2
• Strony: 159-169

Daty

wydano

2000

otrzymano

1999-11-06

poprawiono

2000-04-05

Twórcy

autor

Dariusz Zagrodny

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

Bibliografia

• [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.

Identyfikatory

DOI

10.7151/dmgt.1010