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  • Articles: DFG German National Licenses  (3)
  • Applied Mathematics  (2)
  • interior point optimization methods  (1)
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  • Articles: DFG German National Licenses  (3)
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  • 1
    Electronic Resource
    Electronic Resource
    Optimization Techniques for Solving Elliptic Control Problems with Control and State Constraints: Part 1. Boundary Control (2000)
    Springer
    Computational optimization and applications 16 (2000), S. 29-55 
    Details
    ISSN: 1573-2894
    Keywords: elliptic control problems ; boundary control ; control and state constraints ; discretization techniques ; interior point optimization methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract We study optimal control problems for semilinear elliptic equations subject to control and state inequality constraints. In a first part we consider boundary control problems with either Dirichlet or Neumann conditions. By introducing suitable discretization schemes, the control problem is transcribed into a nonlinear programming problem. It is shown that a recently developed interior point method is able to solve these problems even for high discretizations. Several numerical examples with Dirichlet and Neumann boundary conditions are provided that illustrate the performance of the algorithm for different types of controls including bang-bang and singular controls. The necessary conditions of optimality are checked numerically in the presence of active control and state constraints.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008725519350
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    On the continuation for variational inequalities depending on an eigenvalue parameter (1989)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 11 (1989), S. 95-104 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper we generalize recent theoretical results on the local continuation of parameter-dependent non-linear variational inequalities. The variational inequalities are rather general and describe, for example, the buckling of beams, plates or shells subject to obstacles. Under a technical hypothesis that is satisfied by the simply supported beam, we obtain the existence of a continuation of both the solution and the eigenvalue with respect to a local parameter. A numerical continuation method is presented that easily overcomes turning points. Numerical results are presented for the non-linear beam.
    Additional Material: 2 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670110107
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    Paper (German National Licenses)
    Fulltext
  • 3
    Electronic Resource
    Electronic Resource
    A free boundary problem and stability for the rectangular plate (1990)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 12 (1990), S. 129-138 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In the recent paper [13] we have answered the question of stability for the linear circular plate which is being axially compressed by a force greater than the critical value and contacts a plane obstacle. In this case there are radially symmetric solutions and the contact region is a disk of a smaller radius. This simplified the determination of the critical parameter values for which the plane jumps to another state. For the rectangular plate continuation has to be applied to the variational inequality in order to determine the contact region and evalute the stability criterion. A numerical method is developed for a discretization of the problem and is used to compute the critical load both in the simply supported and the clamped case.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670120204
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    Paper (German National Licenses)
    Fulltext
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