Advertisement

Approximation and Optimization of Polyhedral Discrete and Differential Inclusions

  • Elimhan N. Mahmudov
Part of the Communications in Computer and Information Science book series (CCIS, volume 300)

Abstract

In the first part of the paperoptimization of polyhedral discrete and differential inclusions is considered, the problem is reduced to convex minimization problem and the necessary and sufficient condition for optimality is derived. The optimality conditions for polyhedral differential inclusions based on discrete-approximation problem according to continuous problems are formulated. In particular, boundedness of the set of adjoint discrete solutions and upper semicontinuity of the locally adjoint mapping are proved. In the second part of paper an optimization problem described by convex inequality constraint is studied. By using the equivalence theorem concerning the subdifferential calculus and approximating method necessary and sufficient condition for discrete-approximation problem with inequality constraint is established.

Keywords

Set-valued polyhedral inequality constraint dual cone subdifferential discrete-approximation uniformly bounded upper semicontinuous 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Aubin, J.P., Cellina, A.: Differential inclusions. Grudlehnen der Math. Springer, Wiss. (1984)zbMATHCrossRefGoogle Scholar
  2. 2.
    Mahmudov, E.N., Pshenichnyi, B.N.: Necessary condition of extremum and evasion problem, pp. 3–22. Preprint, Institute Cybernetcis of Ukraine SSR, Kiev (1978)Google Scholar
  3. 3.
    Mahmudov, E.N.: On duality in problems of optimal control described by convex differential inclusions of Goursat-Darboux type. J. Math. Anal. Appl. 307, 628–640 (2005)MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Mahmudov, E.N.: The optimality principle for discrete and the first order partial differential inclusions. J. Math. Anal. Appl. 308, 605–619 (2005)MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    Mahmudov, E.N.: Necessary and sufficient conditions for discrete and differential inclusions of elliptic type. J. Math. Anal. Appl. 323(2), 768–789 (2006)MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    Mahmudov, E.N.: Optimal control of higher order differential in clusions of Bolza type with varying time interval. Nonlinear Analysis-Theory, Method & Applications 69(5-6), 1699–1709 (2008)MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    Mahmudov, E.N.: Duality in the problems of optimal control described by first order partial differential inclusions. Optimization a J. of Math. Program. and Oper. Research 59(4), 589–599 (2010)MathSciNetzbMATHGoogle Scholar
  8. 8.
    Makarov, V.L., Rubinov, A.M.: The Mathematical Theory of Economic Dynamics and Equilibrium, Nauka, Moscow (1977); English transl., Springer, Berlin (1973)Google Scholar
  9. 9.
    Mordukhovich, B.S.: Variational Analysis and Generalized Differentiation, I: Basic Theory; II: Applications, Grundlehren Series. Fundamental Principles of Mathematical Sciences, vol. 330, 331. Springer (2006)Google Scholar
  10. 10.
    Pshenichnyi, B.N.: Convex analysis and extremal problems, Nauka, Moscow (1980)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Elimhan N. Mahmudov
    • 1
  1. 1.Industrial Engineering Department Faculty of ManagementIstanbul Technical UniversityMaçkaTurkey

Personalised recommendations