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  • 1
    Electronic Resource
    Electronic Resource
    A numerical approach to optimization problems with variational inequality constraints (1995)
    Springer
    Mathematical programming 68 (1995), S. 105-130 
    Details
    ISSN: 1436-4646
    Keywords: primary 49B34 ; secondary 90C31 ; 93C30 ; Variational inequalities ; Sensitivity analysis ; Generalized Jacobian
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Optimization problems with variational inequality constraints are converted to constrained minimization of a local Lipschitz function. To this minimization a non-differentiable optimization method is used; the required subgradients of the objective are computed by means of a special adjoint equation. Besides tests with some academic examples, the approach is applied to the computation of the Stackelberg—Cournot—Nash equilibria and to the numerical solution of a class of quasi-variational inequalities.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01585759
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    A Newton method for a class of quasi-variational inequalities (1995)
    Springer
    Computational optimization and applications 4 (1995), S. 5-21 
    Details
    ISSN: 1573-2894
    Keywords: quasi-variational inequality ; implicit complementarity problem ; Newton method ; semismoothness ; generalized Jacobian
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract A variant of the Newton method for nonsmooth equations is applied to solve numerically quasivariational inequalities with monotone operators. For this purpose, we investigate the semismoothness of a certain locally Lipschitz operator coming from the quasi-variational inequality, and analyse the generalized Jacobian of this operator to ensure local convergence of the method. A simplified variant of this approach, applicable to implicit complementarity problems, is also studied. Small test examples have been computed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01299156
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Optimal Design of Trusses Under a Nonconvex Global Buckling Constraint (2000)
    Springer
    Optimization and engineering 1 (2000), S. 189-213 
    Details
    ISSN: 1573-2924
    Keywords: truss design ; buckling ; nonconvex semidefinite programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Technology
    Notes: Abstract We propose a novel formulation of a truss design problem involving a constraint on the global stability of the structure due to the linear buckling phenomenon. The optimization problem is modelled as a nonconvex semidefinite programming problem. We propose two techniques for the numerical solution of the problem and apply them to a series of numerical examples.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1010091831812
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    Paper (German National Licenses)
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