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  • 1
    Electronic Resource
    Electronic Resource
    An iterative two-step algorithm for linear complementarity problems (1994)
    Springer
    Numerische Mathematik 68 (1994), S. 95-106 
    Details
    ISSN: 0945-3245
    Keywords: Mathematics Subject Classification (1991): 65K10
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary. We propose an algorithm for the numerical solution of large-scale symmetric positive-definite linear complementarity problems. Each step of the algorithm combines an application of the successive overrelaxation method with projection (to determine an approximation of the optimal active set) with the preconditioned conjugate gradient method (to solve the reduced residual systems of linear equations). Convergence of the iterates to the solution is proved. In the experimental part we compare the efficiency of the algorithm with several other methods. As test example we consider the obstacle problem with different obstacles. For problems of dimension up to 24\,000 variables, the algorithm finds the solution in less then 7 iterations, where each iteration requires about 10 matrix-vector multiplications.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002110050050
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  • 2
    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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  • 3
    Electronic Resource
    Electronic Resource
    Linear maps majorized by a sublinear map (1975)
    Springer
    Archiv der Mathematik 26 (1975), S. 637-645 
    Details
    ISSN: 1420-8938
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01229793
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    Relaxed outer projections, weighted averages and convex feasibility (1990)
    Springer
    BIT 30 (1990), S. 289-300 
    Details
    ISSN: 1572-9125
    Keywords: F.2.2 ; I.3.5 ; Outer Projections ; Relaxations ; Convex Feasibility Problem ; Row-action Methods ; Block-iterations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A new algorithmic scheme is proposed for finding a common point of finitely many closed convex sets. The scheme uses weighted averages (convex combinations) of relaxed projections onto approximating halfspaces. By varying the weights we generalize Cimmino's and Auslender's methods as well as more recent versions developed by Iusem & De Pierro and Aharoni & Censor. Our approach offers great computational flexibility and encompasses a wide variety of known algorithms as special instances. Also, since it is “block-iterative”, it lends itself to parallel processing.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02017349
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  • 5
    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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  • 6
    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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  • 7
    Book
    Book
    Modern methods of optimization. Proceedings; 378 (1992)
    Berlin u.a. :Springer,
    Details
    Title: Modern methods of optimization. Proceedings; 378
    Contributer: Krabs, Werner , Zowe, Jochem
    Publisher: Berlin u.a. :Springer,
    Year of publication: 1992
    Pages: 348 S.
    Series Statement: Lecture notes in economics and mathematical systems 378
    Type of Medium: Book
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  • 8
    Book
    Book
    Nonsmooth approach to optimization problems with equilibrium constraints : theory, applications and numerical results; 28 (1998)
    Dordrecht u.a. :Kluwer,
    Details
    Title: Nonsmooth approach to optimization problems with equilibrium constraints : theory, applications and numerical results; 28
    Author: Outrata, Jiri
    Contributer: Kocvara, Michal , Zowe, Jochem
    Publisher: Dordrecht u.a. :Kluwer,
    Year of publication: 1998
    Pages: 273 S.
    Series Statement: Nonconvex optimization & its applications 28
    Type of Medium: Book
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