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

Semidefinite programming via image space analysis

Abstract Related Papers Cited by
  • In this paper, we investigate semidefinite programming by using the image space analysis and present some equivalence between the (regular) linear separation and the saddle points of the Lagrangian functions related to semidefinite programming. Some necessary and sufficient optimality conditions for semidefinite programming are also given under some suitable assumptions. As an application, we obtain some equivalent characterizations for necessary and sufficient optimality conditions for linear semidefinite programming under Slater assumption.
    Mathematics Subject Classification: Primary: 90C22, 65K10.

    Citation:

    \begin{equation} \\ \end{equation}
  • [1]

    P. H. Dien, G. Mastroeni, M. Pappalardo and P. H. Quang, Regularity conditions for constrained extremum problems via image space, J. Optim. Theory Appl., 80 (1994), 19-37.doi: 10.1007/BF02196591.

    [2]

    F. Giannessi, Theorems of the alternative and optimality conditions, J. Optim. Theory Appl., 42 (1984), 331-365.doi: 10.1007/BF00935321.

    [3]

    F. Giannessi, Constrained Optimization and Image Space Analysis, Springer, New York, 2005.

    [4]

    F. Giannessi and G. Mastroeni, Separation of sets and Wolfe duality, J. Global Optim., 42 (2008), 401-412.doi: 10.1007/s10898-008-9301-2.

    [5]

    C. Helmberg, Semidefinite programming, European J. Oper. Res., 137 (2002), 461-482.doi: 10.1016/S0377-2217(01)00143-6.

    [6]

    J. Li and N. J. Huang, Image space analysis for vector variational inequalities with matrix inequality constraints and applications, J. Optim. Theory Appl., 145 (2010), 459-477.doi: 10.1007/s10957-010-9691-4.

    [7]

    J. Li and N. J. Huang, Image space analysis for variational inequalities with cone constraints and applications to traffic equilibria, Sci. China Math., 55 (2012), 851-868.doi: 10.1007/s11425-011-4287-5.

    [8]

    D. T. Luc, Theory of Vector Optimization, Springer Verlag, Berlin, 1989.

    [9]

    Y. Nesterov and A. Nemirovskii, Interior-point Polynomial Algorithms in Convex Programming, SIAM Studies in Applied Mathematics, Philadelphia, 1994.doi: 10.1137/1.9781611970791.

    [10]

    R. T. Rockafellar, Convex Analysis, Princeton University Press, Princeton, 1970.

    [11]

    A. Shapiro and K. Scheinberg, Duality and optimality conditions, in Handbook of Semidefinite Programming: Theory, Algorithms and Applications (eds. H. Wolkowicz, R. Saigal and L. Vandenberghe), Kluwer Acad. Publ., 27, Boston, MA, 2000, 67-110.doi: 10.1007/978-1-4615-4381-7_4.

    [12]

    L. Vandenberghe and S. Boyd, Semidefinite programming, SIAM Rev., 38 (1996), 49-95.doi: 10.1137/1038003.

    [13]

    G. Wanka, R. I. Boţ and S. M. Grad, Multiobjective duality for convex semidefinite programming problems, Z. Anal. Anwendungen, 22 (2003), 711-728.doi: 10.4171/ZAA/1169.

    [14]

    S. K. Zhu and S. J. Li, Unified duality theory for constrained extremum problems. Part I: Image space analysis, J. Optim. Theory Appl., 161 (2014), 738-762.doi: 10.1007/s10957-013-0468-4.

    [15]

    J. Zowe and M. Kočvara, Semidefinite programming, in Modern Optimization and its Applications in Engineering (eds. A. Ben-Tal and A. Nemirovski), Haifa (Israel), Technion, 2000.

  • 加载中
SHARE

Article Metrics

HTML views() PDF downloads(193) Cited by(0)

Access History

Other Articles By Authors

Catalog

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return