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  • 1
    Electronic Resource
    Electronic Resource
    Simultaneous simplification of loading and core matrices in N-way PCA: application to chemometric data arrays (1998)
    Springer
    Fresenius' journal of analytical chemistry 361 (1998), S. 15-22 
    Details
    ISSN: 1432-1130
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract In the Tucker3 model of N-way principal components analysis (NPCA), a so-called core matrix describes the possible interactions between components from different modes. For an easy interpretation of solutions, it is necessary to have as few interactions as possible (in conventional PCA of data tables, such interactions can always be avoided). This goal may be realized by various approaches of core matrix transformations. At the same time, it is desirable to have simple component (or loading) matrices. Usually, the simplicity of the core conflicts to a certain degree with the simplicity of the components. The paper demonstrates how the conditional optimization of both goals can be used to find a compromise. For the purpose of illustration, the procedure is first applied to a small three-way data array from heavy metal analysis of tissues in different samples of game. Later, a data array of bigger size from a three-way interlaboratory study is considered.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002160050827
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Metric regularity and quantitative stability in stochastic programs with probabilistic constraints (1999)
    Springer
    Mathematical programming 84 (1999), S. 55-88 
    Details
    ISSN: 1436-4646
    Keywords: Key words: stochastic programming – probabilistic constraints – metric regularity – nonsmooth analysis – quadratic growth – quantitative stability – empirical approximation Mathematics Subject Classification (1991): 90C15, 90C30, 49J52
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s10107980016a
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Characterization of Stability for Cone Increasing Constraint Mappings (1997)
    Springer
    Set-valued analysis 5 (1997), S. 323-349 
    Details
    ISSN: 1572-932X
    Keywords: cone increasing constraints ; nonsmooth analysis ; metric regularity ; chance constraints ; genericity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We investigate stability (in terms of metric regularity) for the specific class of cone increasing constraint mappings. This class is of interest in problems with additional knowledge on some nondecreasing behavior of the constraints (e.g. in chance constraints, where the occurring distribution function of some probability measure is automatically nondecreasing). It is demonstrated, how this extra information may lead to sharper characterizations. In the first part, general cone increasing constraint mappings are studied by exploiting criteria for metric regularity, as recently developed by Mordukhovich. The second part focusses on genericity investigations for global metric regularity (i.e. metric regularity at all feasible points) of nondecreasing constraints in finite dimensions. Applications to chance constraints are given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008629709451
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    Topological characterization of the approximate subdifferential in the finite-dimensional case (1995)
    Springer
    Mathematical methods of operations research 41 (1995), S. 161-173 
    Details
    ISSN: 1432-5217
    Keywords: Approximate subdifferential ; topological properties ; partial approximate subdifferential ; nonsmooth optimization
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract Topological properties of the approximate Subdifferential introduced by Mordukhovich are studied. Apart from formulating a sufficient condition for connectedness, it is shown that, up to homeomorphy, each compact subset of ℝp may occur as the approximate subdifferential of some Lipschitz function. Furthermore, even an exact result is possible when considering the partial approximate Subdifferential, which was introduced as a parametric extension by Jourani and Thibault: Given any compact subset of ℝp, there is a locally Lipschitzian function realizing this set as its partial approximate Subdifferential at some predefined point.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01432653
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    Paper (German National Licenses)
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