ISSN:
1573-2916
Keywords:
Global optimization
;
smooth unconstrained optimization
;
geodesic convexity
;
unimodal function
;
nonlinear coordinate transformation
;
65K05
;
90C30
;
54H00
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract In this two-part article, nonlinear coordinate transformations are discussed in order to simplify global unconstrained optimization problems and to test their unimodality on the basis of the analytical structure of the objective functions. If the transformed problems can be quadratic in some or all the variables, then the optimum can be calculated directly, without an iterative procedure, or the number of variables to be optimized can be reduced. Otherwise, the analysis of the structure can serve as a first phase for solving global unconstrained optimization problems. The first part treats real-life problems where the presented technique is applied and the transformation steps are constructed. The second part of the article deals with the differential geometrical background and the conditions of the existence of such transformations.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01096776
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