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  • Articles: DFG German National Licenses  (2)
  • AMS(MOS): 65N30, 65K10, 49D20  (1)
  • interior point optimization methods  (1)
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  • Articles: DFG German National Licenses  (2)
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  • 1
    Electronic Resource
    Electronic Resource
    On the efficient solution of nonlinear finite element equations. II (1981)
    Springer
    Numerische Mathematik 36 (1981), S. 375-387 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30, 65K10, 49D20 ; CR: 5.17, 5.15
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We consider nonlinear variational inequalities corresponding to a locally convex minimization problem with linear constraints of obstacle type. An efficient method for the solution of the discretized problem is obtained by combining a slightly modified projected SOR-Newton method with the projected version of thec g-accelerated relaxation method presented in a preceding paper. The first algorithm is used to approximately reach in relatively few steps the proper subspace of active constraints. In the second phase a Kuhn-Tucker point is found to prescribed accuracy. Global convergence is proved and some numerical results are presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01395953
    Library Location Call Number Volume/Issue/Year Availability
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    Paper (German National Licenses)
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  • 2
    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)
    Fulltext
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