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  • 1
    Electronic Resource
    Electronic Resource
    Efficient generalized conjugate gradient algorithms, part 2: Implementation (1991)
    Springer
    Journal of optimization theory and applications 69 (1991), S. 139-152 
    Details
    ISSN: 1573-2878
    Keywords: Unconstrained optimization ; hybrid and restart conjugate gradient methods ; limited-memory methods ; inexact line search
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In Part 1 of this paper (Ref. 1), a new, generalized conjugate gradient algorithm was proposed and its convergence investigated. In this second part, the new algorithm is compared numerically with other modified conjugate gradient methods and with limited-memory quasi-Newton methods.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00940465
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  • 2
    Electronic Resource
    Electronic Resource
    Preconditioned low-order Newton methods (1993)
    Springer
    Journal of optimization theory and applications 79 (1993), S. 311-331 
    Details
    ISSN: 1573-2878
    Keywords: Unconstrained optimization ; preconditioning ; lower-or-der Newton methods ; quasi-Newton methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, low-order Newton methods are proposed that make use of previously obtained second-derivative information by suitable preconditioning. When applied to a particular 2-dimensional Newton method (the LS method), it is shown that a member of the Broyden family of quasi-Newton methods is obtained. Algorithms based on this preconditioned LS model are tested against some variations of the BFGS method and shown to be much superior in terms of number of iterations and function evaluations, but not so effective in terms of number of gradient evaluations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00940583
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  • 3
    Electronic Resource
    Electronic Resource
    Family of optimally conditioned quasi-Newton updates for unconstrained optimization (1994)
    Springer
    Journal of optimization theory and applications 83 (1994), S. 421-431 
    Details
    ISSN: 1573-2878
    Keywords: Unconstrained optimization ; quasi-Newton updates ; optimal conditioning ; rankn family
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this note, a general optimal conditioning problem for updates which satisfy the quasi-Newton equation is solved. The new solution is a family of updates which contains other known optimally conditioned updates but also includes new formulas of increased rank. A new factorization formula for the Broyden family and some preliminary numerical results are also given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02190066
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