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  • Articles: DFG German National Licenses  (3)
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  • 1
    Electronic Resource
    Electronic Resource
    The equivalence of strict convexity and injectivity of the gradient in bounded level sets (1991)
    Springer
    Mathematical programming 51 (1991), S. 273-278 
    Details
    ISSN: 1436-4646
    Keywords: Convexity ; injectivity ; generalized gradient ; supporting hyperplane ; affine invariance
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract It is shown that Lipschitzian functions are strictly convex if and only if their generalized gradients are disjoint at distinct interior points of a given bounded level set.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01586939
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    On parametric nonlinear programming (1990)
    Springer
    Annals of operations research 27 (1990), S. 253-283 
    Details
    ISSN: 1572-9338
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract In this tutorial survey we study finite dimensional optimization problems which depend on parameters. It is our aim to work out several basic connections with different mathematical areas. In particular, attention will be paid to unfolding and singularity theory, structural analysis of families of constraint sets, constrained optimization problems and semi-infinite optimization.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02055198
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    Paper (German National Licenses)
    Fulltext
  • 3
    Electronic Resource
    Electronic Resource
    Global Optimization: On Pathlengths in Min-Max Graphs (2000)
    Springer
    Journal of global optimization 17 (2000), S. 161-165 
    Details
    ISSN: 1573-2916
    Keywords: Global optimization ; Gradient flow ; Min-max graphs
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Let f be a smooth nondegenerate real valued function on a finite dimensional, compact and connected Riemannian manifold. The bipartite min-max graph Γ is defined as follows. Its nodes are formed by the set of local minima and the set of local maxima. Two nodes (a local minimum and a local maximum) are connected in Γ by means of an edge if some trajectory of the corresponding gradient flow connects them. Given a natural number k, we construct a function f such that the length of the shortest path in Γ between two specific local minima exceeds k. The latter construction is independent of the underlying Riemannian metric.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1026579317417
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    Paper (German National Licenses)
    Fulltext
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