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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Archiv der Mathematik 75 (2000), S. 233-240 
    ISSN: 1420-8938
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract. We introduce a suitable definition for the horizon function of a convex mapping with values in a Daniell space and prove that the horizon function of a convex composite function coincides with the composite of the corresponding horizon functions.
    Type of Medium: Electronic Resource
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  • 2
    ISSN: 1439-6327
    Keywords: Epinephrine ; Norepinephrine ; Sympathetic system ; Exercise
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Notes: Summary The purpose of this study was to test the reproducibility of plasma norepinephrine (NE) and epinephrine (E) concentrations, at rest and during exercise, in man. Twelve young men were evaluated on two occasions (one week apart) at rest in supine and sitting positions and during dynamic exercise on bicycle ergometer: 5 min at a low intensity workload (heart rate=131–133 bt min−1) and 5 and 20 min at a higher intensity (174–175 bt min−1). Mean plasma NE and E concentrations were not significantly different (p〈0.05) on the two occasions in any of the experimental situations. However large within-subject variations were present, and the “standard errors of a single measurement” corrected for the variability of the catecholamine assay, ranged from 14 to 50% for NE and 14 to 37% for E. These results indicate that the mean plasma NE and E concentrations observed in a group of subjects are reproducible from one week to the other, but that individual plasma NE and E concentrations are not. This lack of reliability of a single determination of plasma catecholamine concentrations might be due to cyclic variations of plasma NE and E concentrations over time.
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    ISSN: 1432-5217
    Keywords: Quasi-inverse ; epi-inverse ; hypo-inverse ; nondecreasing functions ; quasiconvex functions ; convex functions ; duality ; rearrangement ; modulus of continuity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Description / Table of Contents: Zusammenfassung In dieser Arbeit wird systematisch die Umkehrung monoton nichtfallender Funktionenf: ℝ → ℝ ∪ {−∞, +∞} studiert. Die Ergebnisse bilden die Grundlage für eine neue Dualitätstheorie quasikonvexer Probleme [6]. Da jedoch die Fragestellung bei einer ganzen Anzahl weiterer Situationen auftritt, verdient sie eine gesonderte Behandlung. Anwendungen in der Topologie, Wahrscheinlichkeitstheorie, monotonen Umordnungen und in der konvexen Analysis werden aufgezeigt und skizziert.
    Notes: Abstract This work is devoted to a systematic study of the inversion of nondecreasing one variable extended real-valued functions. Its results are preparatory for a new duality theory for quasiconvex problem [6]. However the question arises in a variety of situations and as such deserves a separate treatment. Applications to topology, probability theory, monotone rearrangements, convex analysis are either pointed out or sketched.
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    ISSN: 1573-2878
    Keywords: Convexity ; quasi-convexity ; set convergence ; epi-semicontinuity ; epi-convergence ; value functions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Combining a result on the lower semicontinuity of the intersection of two convex-valued multifunctions and the level set approach of epi-convergence, we obtain results on the epi-upper semicontinuity of the supremum and the sum of two families of quasi-convex functions. As a consequence, we give some condition ensuring the stability of a quasi-convex program under a perturbation of the objective functions and the constraint sets.
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  • 5
    ISSN: 1573-2916
    Keywords: Convex and nonconvex duality ; asymptotical analysis ; approximate subdifferential ; approximate minimizer
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We provide calculus rules for global approximate minima concerning usual operations on functions. The formulas we obtain are then applied to approximate subdifferential calculus. In this way, new results are presented, for example on the approximate subdifferential of a deconvolution, or on the subdifferential of an upper envelope of convex functions.
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  • 6
    ISSN: 1573-2878
    Keywords: Continuous convex sets ; support functions ; convex duality ; coercivity ; recession cones
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Convex functions with continuous epigraph in the sense of Gale and Klée have been studied recently by Auslender and Coutat in a finite-dimensional setting. Here, we provide characterizations of such functionals in terms of the Legendre-Fenchel transformation in general locally convex spaces. Also, we show that the concept of continuous convex sets is of interest in these spaces. We end with a characterization of convex functions on Euclidean spaces with continuous level sets.
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  • 7
    ISSN: 1573-2916
    Keywords: Strict inequality constraint ; Duality ; d.c. Optimization ; Lipschitzian optimization
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We establish a duality formula for the problem Minimize f(x)+g(x) for h(x)+k(x)〈0 where g, k are extended-real-valued convex functions and f, h belong to the class of functions that can be written as the lower envelope of an arbitrary family of convex functions. Applications in d.c. and Lipschitzian optimization are given.
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  • 8
    Electronic Resource
    Electronic Resource
    Springer
    ISSN: 1573-2878
    Keywords: Infimal convolution ; level sum ; connected level set ; quasi-convex function
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A sufficient criterion is established for the infimal convolution of two functions having connected level sets to share the same property without being exact. As a consequence, the infimal convolution of quasiconvex functions on a real line is quasiconvex. However, this is not true on a space of higher dimension, which is illustrated by an example in R 2. Furthermore, connectedness of level sets and local-global minimum properties of functions are analyzed under level addition. Continuity properties of level set maps are also studied in relation with local-global minimum properties.
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  • 9
    Electronic Resource
    Electronic Resource
    Springer
    Mathematical programming 41 (1988), S. 261-278 
    ISSN: 1436-4646
    Keywords: Marginal function ; Fenchel conjugation ; star-difference
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract In this paper a duality is introduced in a concave sense and its relationship with Toland's duality is studied along with several formulas dealing with the conjugates of differences of convex functions.
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  • 10
    Electronic Resource
    Electronic Resource
    Springer
    Set-valued analysis 2 (1994), S. 369-379 
    ISSN: 1572-932X
    Keywords: 49N15 ; inf-convolution ; conjugaison de Fenchel ; sous-différentiel ; dualité convexe ; dualité non convexe
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Résumé La condition de qualification d'Attouch et Brézis est mise à profit pour étudier la sous-différentiabilité de l'inf-convolution de deux fonctions convexes sur un espace de Banach, sans que l'inf-convolution soit nécessairement exacte. Quelques applications de cette condition de qualification à l'optimisation et à la dualité sont présentées.
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