Library

X
feed icon rss

Your email was sent successfully. Check your inbox.

An error occurred while sending the email. Please try again.

Proceed reservation?

Export
  • 1
    Electronic Resource
    Electronic Resource
    The polyadic structure of factorable function tensors with applications to high-order minimization techniques (1986)
    Springer
    Journal of optimization theory and applications 51 (1986), S. 63-94 
    Details
    ISSN: 1573-2878
    Keywords: High-order methods ; factorable functions ; Halley's method ; method of tangent hyperbolas ; Nth derivatives ; polyads ; tensors
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Factorable functions are shown to have arrays ofNth-order derivatives (tensors) which are naturally computed as sums of generalized outer product matrices (polyads). The computational implications of this for high-order minimization techniques (such as Halley's method of tangent hyperbolas) are investigated. A direct derivation of these high-order techniques is also given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00938603
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 2
    Electronic Resource
    Electronic Resource
    Alternative proofs of the convergence properties of the conjugate-gradient method (1974)
    Springer
    Journal of optimization theory and applications 13 (1974), S. 497-518 
    Details
    ISSN: 1573-2878
    Keywords: Conjugate-gradient method ; unconstrained minimization ; superlinearly convergent algorithms ; mathematical programming ; quadratically convergent algorithms
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract For the problem of minimizing an unconstrained function, the conjugate-gradient method is shown to be convergent. If the function is uniformly strictly convex, the ultimate rate of convergence is shown to ben-step superlinear. If the Hessian matrix is Lipschitz continuous, the rate of convergence is shown to ben-step quadratic. All results are obtained for the reset version of the method and with a relaxed requirement on the solution of the stepsize problem. In addition to obtaining sharper results, the paper differs from previously published ones in the mode of proof which contains as a corollary the proof of finiteness of the conjugate-gradient method when applied to a quadratic problem rather than assuming that result.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00933041
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 3
    Electronic Resource
    Electronic Resource
    Projection method for unconstrained optimization (1972)
    Springer
    Journal of optimization theory and applications 10 (1972), S. 57-66 
    Details
    ISSN: 1573-2878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A method of conjugate directions, the projection method, for solving unconstrained minimization problems is presented. Under the assumption of uniform strict convexity, the method is shown to converge to the global minimizer of the unconstrained problem and to have an (n − 1)-step superlinear rate of convergence. With a Lipschitz condition on the second derivatives, the rate of convergence is shown to be a modifiedn-step quadratic one.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00934971
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
Close ⊗
This website uses cookies and the analysis tool Matomo. More information can be found here...