PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
2014 | 43 | nr 3 | 421--437
Tytuł artykułu

Minimax Theorems for ϕ-convex Functions with Applications

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We investigate minimax theorems for ϕ-convex functions. As an application we provide a formula for the ϕ- conjugation of the pointwise maximum of ϕ- convex functions. (original abstract)
Rocznik
Tom
43
Numer
Strony
421--437
Opis fizyczny
Twórcy
  • Systems Research Institute of the Polish Academy of Sciences
autor
  • Warsaw University of Technology
Bibliografia
  • AUBIN, J.P. (1998), Optima and Equilibria. Springer, New York-Berlin- Heidelberg.
  • BOT˛, R.I., WANKA, G. (2008), The conjugate of the pointwise maximum of two convex functions revisited. J. Glob. Optim. 41, 625-632.
  • BURACHIK, R.S., JEYAKUMAR, V. (2005), A new geometric condition for Fenchel's duality in infinite dimensions. Math. Program. 104B, 229-233.
  • BURACHIK, R. S., RUBINOV, A. (2008), On abstract convexity and set valued analysis. J. Nonlinear and Convex Analysis 9, 105-123.
  • DOLECKI, S., KURCYUSZ, S. (1978), On ϕ-convexity in extremal problems. SIAM J. Control and Optimization 16, 277-300.
  • EKELAND, I., TEMAM, R. (1976), Convex Analysis and Variational Problems. North-Holland, Amsterdam.
  • FAN, K. (1953), Minimax theorems. Proc. Nat. Acad. Sci. 39, 42-47.
  • FITZPATRICK, S.P., SIMONS, S. (2000), On the pointwise maximum of convex functions. Proc. Am. Math. Soc. 128, 3553-3561.
  • KINDLER, J. (1990), On a minimax theorem of Terkelsen's. Arch. Math. 55, 573-583.
  • KINDLER, J., TROST, R. (1989), Minimax theorems for interval spaces. Act. Mat. Hung. 54, 39-49.
  • JEYAKUMAR, V., RUBINOV, A.M., WU, Z.Y. (2007), Generalized Fenchel's conjugation formulas and duality for abstract convex functions. J. Optim. Theory Appl. 132, 441-458.
  • NAGATA, J.I. (1985), Modern General Topology. North-Holland, Amsterdam.
  • VON NEUMANN, J. (1928), Zur Theorie der Gesellschaftspiele. Math. Ann. 100, 295-320. For an English translation see: On the theory of games of strategy. Contributions to the theory of games 4, Princeton. Univ. Press (1959), 13-42.
  • PALLASCHKE, D., ROLEWICZ, S. (1997), Foundations of Mathematical Optimization. Kluwer Academic, Dordecht.
  • RICCERI, B. (1993), Some topological mini-max theorems via an alternative principle for multifunctions. Arch. Math. 60, 367-377.
  • RICCERI, B. (2008), Recent Advances in Minimax Theory and Applications. Pareto Optimality, Game Theory And Equilibria. Springer Optimization and Its Applications 17, 23-52.
  • ROLEWICZ, S. (2003), ϕ-convex functions defined on a metric spaces. J. Math. Sci. 115, 2631 2652.
  • RUBINOV, A.M. (2000), Abstract Convexity and Global Optimization. Kluwer Academic, Dordrecht.
  • SIMONS, S. (1972), Maximinimax, minimax and antiminimax theorems and a result of R.C. James. Pacific Journal of Mathematics 40 (3), 709-718.
  • SIMONS, S. (1990), On Terkelson's minimax theorem. Bull. Inst. Math. Acad. Sinica 18, 35-39.
  • SIMONS, S. (1994), A flexible minimax theorem. Acta Math. Hungar. 63, 119- 132.
  • SIMONS, S. (1995), Minimax theorems and their proofs. In: D.-Z. Du and P. M. Pardalos, eds., Minimax and Applications. Kluwer Academic Publishers, 1-23.
  • SION, M. (1958), On general minimax theorems. Pac. J. Math. 8, 171-176.
  • SINGER, I. (1997), Abstract Convex Analysis. Wiley-Interscience, New York.
  • SOLTAN, V.P. (1984), Introduction to Axiomatic Theory of Convexity (in Russian). Śtiinca, Kishiniev.
  • STEFANESCU, A. (1985), A general min-max theorem. Optimization 16, 405- 413.
  • STEFANESCU, A. (2007), The minimax equality; sufficient and necessary conditions. Acta Math. Sinica, English Series 23, 677-684.
  • TERKELSEN, F. (1972), Some Minimax Theorems. Math. Scand. 31, 405-413.
  • TUY, I. (1974), On a general minimax theorem. Soviet Math. Dokl. 15, 1689- 1693.
  • WU, W.-T. (1959), A remark on the fundamental theorem in the theory of games. Sci. Rec. New Set. 3, 229-233.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.ekon-element-000171511172

Zgłoszenie zostało wysłane

Zgłoszenie zostało wysłane

Musisz być zalogowany aby pisać komentarze.
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.