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Characterization of Stability for Cone Increasing Constraint Mappings (1997)

Henrion, René

Springer

Set-valued analysis 5 (1997), S. 323-349

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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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Latent features with maximal correlation between two equal sets of variables (1990)

Henrion, René ; Henrion, Günter

New York, NY : Wiley-Blackwell

Journal of Chemometrics 4 (1990), S. 187-189

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ISSN: 0886-9383

Keywords: Analysis of correlation ; Common latent features ; Trace elements in human tissues ; Chemistry ; Analytical Chemistry and Spectroscopy

Source: Wiley InterScience Backfile Collection 1832-2000

Topics: Chemistry and Pharmacology

Notes: If in two data tables X and Y objects are characterized by the same variables (measured at different occasions), then looking for common latent features should be more appropriate than choosing latent features in X and Y separately (e.g. as in canonical correlation or PLS). The procedure to be proposed here is a slight modification of the method of linear characteristics (according to De Groot and Li) by disclaiming the assumption of equal inner-block covariance matrices. In order to find weights defining a latent feature with maximal correlation between X and Y, a system of non-linear equations has to be solved. The procedure is applied to the investigation of heavy metal concentrations in different human tissues.