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  • Articles: DFG German National Licenses  (2)
  • 53 A 10  (1)
  • Semidefinite programming  (1)
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  • Articles: DFG German National Licenses  (2)
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Years
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  • 1
    Electronic Resource
    Electronic Resource
    Minimal surfaces with prescribed topological type on a Schwarzian chain inM c 3 (1993)
    Springer
    Annals of global analysis and geometry 11 (1993), S. 331-344 
    Details
    ISSN: 1572-9060
    Keywords: Minimal surfaces ; quasi-minimal surfaces ; variational principle ; Schwarzian chain ; 53 A 10 ; 49 Q 05 ; 58 E 12
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Similar to the investigations of unstable polygonal minimal surfaces by Courant [1] we introduce here a variational principle for the free boundary problem with prescribed topological type which produces minimal surfaces in Riemannian manifolds with constant curvature. For special boundary configurations the surfaces have no branch points. The approach can be applied to numerical algorithms since it is constructive.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00773549
    Library Location Call Number Volume/Issue/Year Availability
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    Paper (German National Licenses)
    Fulltext
  • 2
    Electronic Resource
    Electronic Resource
    A New Semidefinite Programming Bound for Indefinite Quadratic Forms Over a Simplex (1999)
    Springer
    Journal of global optimization 14 (1999), S. 357-364 
    Details
    ISSN: 1573-2916
    Keywords: Global optimization ; Nonconvex quadratic programming ; Semidefinite programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The paper describes a method for computing a lower bound of the global minimum of an indefinite quadratic form over a simplex. The bound is derived by computing an underestimator of the convex envelope by solving a semidefinite program (SDP). This results in a convex quadratic program (QP). It is shown that the optimal value of the QP is a lower bound of the optimal value of the original problem. Since there exist fast (polynomial time) algorithms for solving SDP's and QP's the bound can be computed in reasonable time. Numerical experiments indicate that the relative error of the bound is about 10 percent for problems up to 20 variables, which is much better than a known SDP bound.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008315627883
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
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