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  • 1
    Electronic Resource
    Electronic Resource
    Variable metric methods in Hilbert space with applications to control problems (1976)
    Springer
    Journal of optimization theory and applications 19 (1976), S. 381-400 
    Details
    ISSN: 1573-2878
    Keywords: Variable metric methods ; optimization theorems ; Hilbert spaces ; control theory
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper is concerned with some of the most powerful methods of minimizing functionals on Hilbert space. It is established that certain classes of these methods are equivalent and their convergence is proved for certain nonquadratic functionals on a Hilbert space. A computational study of these methods applied to a control problem is also included with particular reference to the equivalence of methods mentioned above.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00941483
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Direct-prediction quasi-Newton methods in Hilbert space with applications to control problems (1977)
    Springer
    Journal of optimization theory and applications 21 (1977), S. 199-211 
    Details
    ISSN: 1573-2878
    Keywords: Variable-metric methods ; optimization theorems ; Hilbert spaces ; control theory
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, the Hilbert-space analogue of a result of Huang, that all the methods in the Huang class generate the same sequence of points when applied to a quadratic functional with exact linear searches, is established. The convergence of a class of direct prediction methods based on some work of Dixon is then proved, and these methods are then applied to some control problems. Their performance is found to be comparable with methods involving exact linear searches.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00932520
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    Paper (German National Licenses)
    Fulltext
  • 3
    Electronic Resource
    Electronic Resource
    Direct prediction methods in Hilbert space with applications to control problems (1977)
    Springer
    Journal of optimization theory and applications 22 (1977), S. 399-415 
    Details
    ISSN: 1573-2878
    Keywords: Variable-metric methods ; optimization theorems ; Hilbert spaces ; control theory
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, the convergence of variable-metric methods without line searches (direct prediction methods) applied to quadratic functionals on a Hilbert space is established. The methods are then applied to certain control problems with both free endpoints and fixed endpoints. Computational results are reported and compared with earlier results. The methods discussed here are found to compare favorably with earlier methods involving line searches and with other direct prediction quasi-Newton methods.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00932863
    Library Location Call Number Volume/Issue/Year Availability
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    Paper (German National Licenses)
    Fulltext
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