\`x^2+y_1+z_12^34\`
Advanced Search
Article Contents
Article Contents

Necessary optimality conditions for an integro-differential Bolza problem via Dubovitskii-Milyutin method

  • * Corresponding author: Stanisław Walczak

    * Corresponding author: Stanisław Walczak

A tribute to Helmut Maurer, Urszula Ledzewicz and Heinz Schättler.
The second author has a great satisfaction to be a supervisor of the doctoral dissertation of Professor Urszula Ledzewicz

Abstract / Introduction Full Text(HTML) Related Papers Cited by
  • In the paper, we derive a maximum principle for a Bolza problem described by an integro-differential equation of Volterra type. We use the Dubovitskii-Milyutin approach.

    Mathematics Subject Classification: Primary: 49K21, 34K35.

    Citation:

    \begin{equation} \\ \end{equation}
  • 加载中
  • [1] H. Brezis, Functional Analysis, Sobolev Spaces and Partial Differential Equations, Springer, New York, 2011.
    [2] M. Ya. Dubovitskii and A. A. Milyutin, The extremum problem in the presence of constraints, Dokl. Acad. Nauk SSSR, 149 (1963), 759-762. 
    [3] M. Ya. Dubovitskii and A. A. Milyutin, Extremum problems in the presence of constraints, Zh. Vychisl. Mat. i Mat. Fiz., 5 (1965), 395-453. 
    [4] I. W. Girsanow, Lectures on Mathematical Theory of Extremum Problems, Springer, New York, 1972.
    [5] D. Idczak and S. Walczak, Application of a global implicit function theorem to a general fractional integro-differential system of Volterra type, Journal of Integral Equations and Applications, 27 (2015), 521-554. 
    [6] D. Idczak, Optimal control of a coercive Dirichlet problem, SIAM J. Control Optim., 36 (1998), 1250-1267.  doi: 10.1137/S0363012997296341.
    [7] D. IdczakA. Skowron and S. Walczak, On the diffeomorphisms between Banach and Hilbert spaces, Advanced Nonlinear Studies, 12 (2012), 89-100.  doi: 10.1515/ans-2012-0105.
    [8] D. Idczak, A. Skowron and S. Walczak, Sensitivity of a fractional integrodifferential Cauchy problem of Volterra type, Abstract and Applied Analysis, 2013 (2013), Article Id 129478, 8 pages. doi: 10.1155/2013/129478.
    [9] A. D. Ioffe and V. M. Tikhomirov, Theory of Extremum Problems, North-Holland, 1979.
    [10] U. Ledzewicz, A necessary condition for a problem of optimal control with equality and inequality constraints, Control and Cybernetics, 14 (1985), 351-360. 
    [11] U. Ledzewicz, On some specification of the Dubovitskii-Milyutin method, Nonlinear Analysis: theory, methods and Applications, 10 (1986), 1367-1371.  doi: 10.1016/0362-546X(86)90107-0.
    [12] U. Ledzewicz, Application of the method of contractor directions to the Dubovitskii-Milyutin formalism, Journal of Mathematical Analysis and Applications, 125 (1987), 174-184.  doi: 10.1016/0022-247X(87)90172-7.
    [13] U. Ledzewicz, Application of some specitfication of the Dubovitskii-Milyutin method to problems of optimal control, Nonlinear Analysis: Theory, Methods and Applications, 10 (1986), 1367-1371.  doi: 10.1016/0362-546X(86)90107-0.
    [14] U. LedzewiczH. Schättler and S. Walczak, Stability of elliptic optimal control problems, Comput. Math. Appl., 41 (2001), 1245-1256.  doi: 10.1016/S0898-1221(01)00095-5.
    [15] V. Volterra, Sulle equazioni integro-differenziali, R. C. Acad. Lincei (5), 18 (1909), 167-174.
    [16] V. Volterra, Sulle equazioni della elettrodinamica, R. C. Acad. Lincei (5), 18 (1909), 203-211.
    [17] V. Volterra, Sulle equazioni integro-differenziali della teoria dell’elasticita, R. C. Acad. Lincei (5), 18 (1909), 296-301.
    [18] V. Volterra, Equazioni integro-differenziali della elasticita nel caso della isotropia, R. C. Acad. Lincei (5), 18 (1909), 577-586.
  • 加载中
SHARE

Article Metrics

HTML views(2098) PDF downloads(245) Cited by(0)

Access History

Other Articles By Authors

Catalog

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return