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  • 1
    Electronic Resource
    Electronic Resource
    Approximation to a set-valued mapping, I: A proposal (1986)
    Springer
    Applied mathematics & optimization 14 (1986), S. 203-214 
    Details
    ISSN: 1432-0606
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Given a multivalued mappingF, we address the problem of finding another multivalued mappingS that agrees locally withF. We limit ourselves to the case whenF(x) is convex compact for eachx. We propose anS obtained by linearizing the support function ofF(x) and give conditions under which thisS approximatesF in the sense of Hausdorff distance. We show equality betweenS and other proposals obtained from tangent cones to the graph ofF. Finally, we apply these results to the approximate subdifferential of a convex function.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01442236
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Hunting for a Smaller Convex Subdifferential (1997)
    Springer
    Journal of global optimization 10 (1997), S. 305-326 
    Details
    ISSN: 1573-2916
    Keywords: Clarke subdifferential ; Michel–Penot subdifferential ; quasidifferential ; convexificator ; mean-value theorem ; nonsmooth analysis.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Certain useful basic results of the gradient (in the smooth case), the Clarkesubdifferential, the Michel–Penot subdifferential, which is also known asthe "small" subdifferential, and the directional derivative(in the nonsmooth case) are stated and discussed. One of the advantages ofthe Michel–Penot subdifferential is the fact that it is in general "smaller"than the Clarke subdifferential. In this paper it is shown that there existsubdifferentials which may be smaller than the Michel–Penot subdifferentialandwhich have certain useful calculus. It isfurther shown that in the case of quasidifferentiability, the Michel–Penotsubdifferential enjoys calculus whichhold for the Clarke subdifferential only in the regular case.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008246130864
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    On the maximization of a certain nondifferentiable function (1971)
    Springer
    Journal of optimization theory and applications 7 (1971), S. 75-89 
    Details
    ISSN: 1573-2878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Let us consider a function $$\begin{gathered} \varphi (z) = \min \max f_{ij} (z), \hfill \\ \begin{array}{*{20}c} --- \\ {j \in 1,N} \\ \end{array} \begin{array}{*{20}c} --- \\ {j \in 1,N_j } \\ \end{array} \hfill \\ \end{gathered} $$ where the functionsf ij(z) are supposed to be continuously differentiable and real-valued on a set Ω ofE n,z∂E n. The problem is to find maxzɛΩϕ(z). In this paper, it is proved that ϕ(z) is directionally differentiable. A necessary condition for a maximum is derived, and some numerical algorithms for maximizing ϕ are suggested. The results obtained can be applied for solving some problems in mathematical programming and control theory.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00945418
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  • 4
    Electronic Resource
    Electronic Resource
    Representation of the Clarke subdifferential for a regular quasidifferentiable function (1995)
    Springer
    Journal of optimization theory and applications 87 (1995), S. 553-561 
    Details
    ISSN: 1573-2878
    Keywords: Lipschitz functions ; Clarke subdifferential ; quasidifferential
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A class of Lipschitz quasidifferentiable functions is described for which the exact representation of the Clarke subdifferential in terms of a quasidifferential holds. The sufficient conditions formulated are different from those previously established by Rubinov and Akhundov.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02192133
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    Paper (German National Licenses)
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  • 5
    Electronic Resource
    Electronic Resource
    Book review (1995)
    Springer
    Journal of global optimization 6 (1995), S. 321-323 
    Details
    ISSN: 1573-2916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01099468
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    Paper (German National Licenses)
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  • 6
    Electronic Resource
    Electronic Resource
    Theorem on an implicit function in quasidifferential calculus (1996)
    Springer
    Journal of mathematical sciences 78 (1996), S. 556-567 
    Details
    ISSN: 1573-8795
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02363856
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  • 7
    Book
    Book
    Quasidifferential calculus /; 29 (1986)
    Details
    Title: Quasidifferential calculus /; 29
    Contributer: Demyanov, V. F.
    Year of publication: 1986
    Pages: VIII, 221 S.
    Series Statement: Mathematical programming 29
    Type of Medium: Book
    Language: English
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    ZIB Catalog
    Zuse Institute Berlin get availability status
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