Skip to main content
Advances in Continuous and Discrete Models

Theory and Modern Applications

Download PDF
  • Research Article
  • Open access
  • Published:

Optimization Of discrete and differential inclusions of Goursat-Darboux type with state constraints

Advances in Difference Equations volume 2006, Article number: 041962 (2006) Cite this article

Abstract

Necessary and sufficient conditions of optimality under the most general assumptions are deduced for the considered and for discrete approximation problems. Formulation of sufficient conditions for differential inclusions is based on proved theorems of equivalence of locally conjugate mappings.

[1234567891011121314151617181920]

References

  1. Agarwal RP, Grace SR, O'Regan D: Oscillation of higher order difference equations via comparison. Glasnik Matematički. Serija III 2004,39(59)(2):287–299.

    Article  MathSciNet  MATH  Google Scholar 

  2. Barbu V: The time optimal control of variational inequalities. Dynamic programming and the maximum principle. In Recent Mathematical Methods in Dynamic Programming (Rome, 1984), Lecture Notes in Math.. Volume 1119. Springer, Berlin; 1985:1–19. 10.1007/BFb0074777

    Chapter  Google Scholar 

  3. Butkovskiĭ AG: Theory of Optimal Control of Systems with Distributed Parameters. Nauka, Moscow; 1965:474. English translation in Distributed control systems, American Elsevier, New York, 1969

    Google Scholar 

  4. Clarke FH, Ledyaev YuS, Radulescu ML: Approximate invariance and differential inclusions in Hilbert spaces. Journal of Dynamical and Control Systems 1997,3(4):493–518.

    MathSciNet  MATH  Google Scholar 

  5. Demianov VF, Vasilev LV: Nondifferentiable Optimisation. Optimization Software, New York; 1985.

    Book  Google Scholar 

  6. Ekeland I, Temam R: Convex Analysis and Variational Problems. MIR, Moscow; 1979:399.

    MATH  Google Scholar 

  7. Fornosini E, Marchesini G: Doubly indexed dynamical systems. Mathematical Systems Theory 1978.,12(1):

    Google Scholar 

  8. Ioffe AD, Tikhomirov VM: Theory of Extremal Problems. Nauka, Moscow; 1974:479. English translation in North-Holland, Amsterdam, 1978

    Google Scholar 

  9. Kaczorek T: Two-Dimensional Linear Systems, Lecture Notes in Control and Information Sciences. Volume 68. Springer, Berlin; 1985:x+398.

    Google Scholar 

  10. Kuang H-W: Minimum time function for differential inclusion with state constraints. Mathematica Applicata 2000,13(2):31–36.

    MathSciNet  MATH  Google Scholar 

  11. Lions J-L: Contrôle optimal de systèmes gouvernés par des équations aux dérivées partielles. Dunod, Gauthier-Villars, Paris; 1968:xiii+426.

    MATH  Google Scholar 

  12. Mahmudov EN: On duality in optimal control problems described by convex discrete and differcutial inclusious. Avtomatika i Telemekhanika 1987, (2):13–25. English translation in Automation and Remote Control 48 (1987)

    Google Scholar 

  13. Mahmudov EN: Optimization of discrete inclusions with distributed parameters. Optimization 1990,21(2):197–207. 10.1080/02331939008843535

    Article  MathSciNet  MATH  Google Scholar 

  14. Mahmudov EN: Mathematical Analysis and Applications. Papatya, Istanbul; 2002:392.

    Google Scholar 

  15. Makarov VL, Rubinov AM: Mathematical Theory of Economic Dynamics and Equilibria. Nauka, Moscow; 1973:335. English translation in Springer, Berlin, 1977

    Google Scholar 

  16. Mordukhovich BS: Optimal Control of Nonconvex Discrete and Differential Inclusions. Sociedad Matematica Mexicana, Mexico; 1998:vi + 324.

    Google Scholar 

  17. Mordukhovich BS: Optimal control of difference, differential, and differential-difference inclusions. Journal of Mathematical Sciences (New York) 2000,100(6):2613–2632. 10.1007/BF02672708

    Article  MathSciNet  Google Scholar 

  18. Pšeničnyĭ BN: Convex Analysis and Extremal Problems, Series in Nonlinear Analysis and Its Applications. Nauka, Moscow; 1980:320.

    Google Scholar 

  19. Rockafellar RT: Convex Analysis. Princeton University Press, New Jersey; 1972.

    MATH  Google Scholar 

  20. Tikhonov AN, Samarskii AA: The Equations of Mathematical Physics. 3rd edition. Nauka, Moscow; 1966. English translation of 2nd ed., vols, 1, 2, Holden-Day, California, 1964, 1967

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Industrial Engineering, Engineering Faculty, Istanbul University, Avcilar, Istanbul, 34850, Turkey

    Elimhan N Mahmudov

Authors
  1. Elimhan N Mahmudov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Elimhan N Mahmudov.

Rights and permissions

Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License ( https://creativecommons.org/licenses/by/2.0 ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Reprints and permissions

About this article

Cite this article

Mahmudov, E.N. Optimization Of discrete and differential inclusions of Goursat-Darboux type with state constraints. Adv Differ Equ 2006, 041962 (2006). https://doi.org/10.1155/ADE/2006/41962

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1155/ADE/2006/41962

Keywords