ISSN:
1573-2878
Keywords:
Unconstrained optimization
;
collinear scaling method
;
conic models
;
quasi-Newton algorithms
;
numerical algorithms
;
non-linear programming
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract An appealing approach to the solution of nonlinear optimization problems based on conic models of the objective function has been recently introduced by Davidon. It leads to a broad class of algorithms which, in some sense, can be considered to generalize the existing quasi-Newton algorithms. One particular member of this class has been deeply examined by Sorensen, who has proved some interesting theoretical properties. A new interpretation of this algorithm is suggested in this paper from a more straightforward and somewhat familiar point of view. In addition, numerical experiments have been carried out to compare the Sorensen algorithm with a straightforward BFGS implementation of the classical quasi-Newton method with the final aim to assess the real merits and benefits of the new algorithm. Although some challenging test functions are used in computational experiments, the results are not particularly favorable to the new algorithm. As a matter of fact they do not exhibit any jump of quality, as it might be expected. Lastly, it is pointed out that a difficulty may affect the new method in situations in which it is necessary to exploit the special structure of large-scale problems.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00934743
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