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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Annals of global analysis and geometry 11 (1993), S. 331-344 
    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
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Journal of global optimization 18 (2000), S. 337-356 
    ISSN: 1573-2916
    Keywords: Global optimization ; Nonconvex quadratic programming ; Lagrangian relaxation ; Optimality cuts ; Duality gap
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A central problem of branch-and-bound methods for global optimization is that often a lower bound do not match with the optimal value of the corresponding subproblem even if the diameter of the partition set shrinks to zero. This can lead to a large number of subdivisions preventing the method from terminating in reasonable time. For the all-quadratic optimization problem with convex constraints we present optimality cuts which cut off a given local minimizer from the feasible set. We propose a branch-and-bound algorithm using optimality cuts which is finite if all global minimizers fulfill a certain second order optimality condition. The optimality cuts are based on the formulation of a dual problem where additional redundant constraints are added. This technique is also used for constructing tight lower bounds. Moreover we present for the box-constrained and the standard quadratic programming problem dual bounds which have under certain conditions a zero duality gap.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Journal of global optimization 14 (1999), S. 357-364 
    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
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  • 4
    Title: Relaxation and decomposition methods for mixed integer nonlinear programming /; 152
    Author: Nowak, Ivo
    Edition: 1
    Publisher: Basel [u.a.] :Birkhäuser,
    Year of publication: 2005
    Pages: XVI, 213 S.
    Series Statement: International series of numerical mathematics 152
    ISBN: 3-7643-7238-9 , 978-3-7643-7238-5
    Type of Medium: Book
    Language: English
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  • 5
    Publication Date: 2020-08-05
    Description: We propose an efficient column generation method to minimize the probability of delay propagations along aircraft rotations. In this way, delay resistant schedules can be constructed. Computational results for large-scale real-world problems demonstrate substantial punctuality improvements. The method can be generalized to crew and integrated scheduling problems.
    Keywords: ddc:510
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/pdf
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