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  • 1
    Electronic Resource
    Electronic Resource
    Optimal shape design for systems governed by variational inequalities, part 3: Necessary conditions in the elliptic case (1992)
    Springer
    Journal of optimization theory and applications 74 (1992), S. 273-304 
    Details
    ISSN: 1573-2878
    Keywords: Optimal shape design ; variational inequalities ; mapping method ; optimal control for variational inequalities ; optimality conditions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract General optimality conditions are obtained for optimal shape design for systems governed by a class of elliptic variational inequalities. The conditions are established by making use of the necessary conditions for optimal control of systems governed by strongly monotone variational inequalities. These conditions are then applied to an electrochemical machining problem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00940895
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Optimal shape design for systems governed by variational inequalities, part 1: Existence theory for the elliptic case (1991)
    Springer
    Journal of optimization theory and applications 69 (1991), S. 351-371 
    Details
    ISSN: 1573-2878
    Keywords: Optimal shape design ; variational convergence theory ; elliptic variational inequalities ; existence theorems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Some general existence results for optimal shape design problems for systems governed by elliptic variational inequalities are established by the mapping method and variational convergence theory. Then, an existence theorem is given for the optimal shape for an electrochemical machining problem, in which the cost functional is not lower semicontinuous, by extending the general results to this case. Furthermore, this problem is approximated by a set of optimal shape design problems which have more smooth cost functionals and are easier to handle computationally.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00940649
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  • 3
    Electronic Resource
    Electronic Resource
    Optimal shape design for systems governed by variational inequalities, part 2: Existence theory for the evolution case (1991)
    Springer
    Journal of optimization theory and applications 69 (1991), S. 373-396 
    Details
    ISSN: 1573-2878
    Keywords: Optimal shape design ; variational convergence theory ; evolution variational inequalities ; existence theorems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Some general existence results for optimal shape design problems for systems governed by parabolic variational inequalities are established by the mapping method and variational convergence theory. Then, an existence theorem is given for the optimal shape for an electrochemical machining problem, in which the cost functional is not lower semicontinuous, by extending the general results to this case. Furthermore, this problem is approximated by a set of optimal shape design problems which have more smooth cost functionals and are easier to handle computationally.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00940650
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    Paper (German National Licenses)
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