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  • 1
    Electronic Resource
    Electronic Resource
    Lower semicontinuity in domain optimization problems (1988)
    Springer
    Journal of optimization theory and applications 59 (1988), S. 407-422 
    Details
    ISSN: 1573-2878
    Keywords: Lower semicontinuity ; domain optimization ; boundary-value problems ; Dirichlet problems ; Neumann problems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In the present paper, the lower semicontinuity of certain classes of functionals is studied when the domain of integration, which defines the functionals, is not fixed. For this purpose, a certain class of domains introduced by Chenais is employed. For this class of domains, a basic lemma is proved that plays an essential role in the derivations of the lower-semicontinuity theorems. These theorems are applied to the study of the existence of the optimal domain in domain optimization problems; a boundary-value problem of Neumann type or Dirichlet type is the main constraint in these optimization problems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00940307
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  • 2
    Electronic Resource
    Electronic Resource
    Second-order necessary conditions in a domain optimization problem (1990)
    Springer
    Journal of optimization theory and applications 65 (1990), S. 223-244 
    Details
    ISSN: 1573-2878
    Keywords: Domain optimization ; shape optimal design ; distributed-parameter systems ; boundary-value problems ; first and second variations ; first-order and second-order necessary conditions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Second-order necessary conditions of the Kuhn-Tucker type for optimality in a domain optimization problem are studied. The second variation, corresponding to a boundary variation, of the solution to a boundary-value problem is shown to exist and is given as the solution of a boundary-value problem of the same type. The boundary data are shown to be given in terms of the solution and the first variation of the solution. From these results, the second variation of the objective function is calculated to derive second-order necessary conditions of the Kuhn-Tucker type.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01102343
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  • 3
    Electronic Resource
    Electronic Resource
    Second-order numerical method for domain optimization problems (1990)
    Springer
    Journal of optimization theory and applications 67 (1990), S. 533-550 
    Details
    ISSN: 1573-2878
    Keywords: Second-order numerical methods ; domain optimization ; boundary-value problems ; Newton method ; adjoint variables
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper is concerned with a second-order numerical method for shape optimization problems. The first variation and the second variation of the objective functional are derived. These variations are discretized by introducing a set of boundary-value problems in order to derive the second-order numerical method. The boundary-value problems are solved by the conventional finite-element method.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00939648
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