Nonlinear Problems in Mathematical Programming and Optimal Control

  • Dumitru Motreanu
Part of the Springer Optimization and Its Applications book series (SOIA, volume 35)


Necessary conditions of optimality are obtained for general mathematical programming problems on a product space. The cost functional is locally Lipschitz and the constraints are expressed as inclusion relations with unbounded linear operators and multivalued term. The abstract result is applied to an optimal control problem governed by an elliptic differential inclusion.


Linear Operator Optimal Control Problem Multivalued Mapping Tangent Cone Nonlinear Programming Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    S. Aizicovici, D. Motreanu and N. H. Pavel, Nonlinear programming problems associated with closed range operators, Appl. Math. Optim. 40 (1999), 211–228.MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    S. Aizicovici, D. Motreanu and N. H. Pavel, Fully nonlinear programming problems with closed range operators, in Differential Equations and Control Theory (S. Aizicovici and N. H. Pavel, eds.), Lecture Notes Pure Appl. Math., Vol. 225, M. Dekker, New York, 2001, pp. 19–30.Google Scholar
  3. 3.
    S. Aizicovici, D. Motreanu and N. H. Pavel, Nonlinear mathematical programming and optimal control, Dynamics of Continuous, Discrete and Impulsive Systems 11 (2004), 503–524.MATHMathSciNetGoogle Scholar
  4. 4.
    A. Ambrosetti and G. Prodi, A Primer of Nonlinear Analysis, Cambridge University Press, Cambridge, 1995.MATHGoogle Scholar
  5. 5.
    J. Baier and J. Jahn, On subgradients of set-valued maps, J. Optim. Theory Appl. 100 (1999), 233–240.MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    H. Brézis, Analyse fonctionnelle. Théorie et applications, Masson, Parris, 1992.Google Scholar
  7. 7.
    F. H. Clarke, Optimization and Nonsmooth Analysis, John Wiley and Sons, New York, 1983.MATHGoogle Scholar
  8. 8.
    S. C. Gao and N. H. Pavel, Optimal control of a functional equation associated with closed range self-adjoint operators, Proc. Amer. Math. Soc. 126 (1998), 2979–2986.MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    G. Isac, V. A. Bulavski and V. V. Kalashnikov, Complementarity, Equilibrium, Efficiency and Economics, Kluwer Academic Publishers, Dordrecht, 2002.MATHGoogle Scholar
  10. 10.
    G. Isac and A. A. Khan, Dubovitskii-Milyutin approach in set-valued optimization, SIAM J. Control Optim. 126 (2008), 144–162.CrossRefMathSciNetGoogle Scholar
  11. 11.
    V. K. Le and D. Motreanu, Some properties of general minimization problems with constraints, Set-Valued Anal. 14 (2006), 413–424.MATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    D. Motreanu and N. H. Pavel, Tangency, Flow-Invariance for Differential Equations and Optimization Problems, Marcel Dekker, New York, 1999.MATHGoogle Scholar
  13. 13.
    M. D. Voisei, First-order necessary optimality conditions for nonlinear optimal control problems, PanAmer. Math. J. 14 (2004), 1–44.MATHMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of PerpignanPerpignanFrance

Personalised recommendations