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  • 1
    Electronic Resource
    Electronic Resource
    A general cone decomposition theory based on efficiency (1994)
    Springer
    Mathematical programming 65 (1994), S. 1-20 
    Details
    ISSN: 1436-4646
    Keywords: Efficient decomposition ; Moreau decomposition ; partially ordered vector spaces
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract LetK 1 andK 2 be two convex cones in some common vector space. This paper is concerned with the question of finding a ‘good’ decomposition, with respect toK 1 andK 2, of a given element of the Minkowski sumK 1 +K 2. We propose the criterion of efficiency as a measure for the quality of a decomposition. This criterion allows us to set up a framework from which a general cone decomposition theory is then derived.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01581687
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Yuan's alternative theorem and the maximization of the minimum eigenvalue function (1994)
    Springer
    Journal of optimization theory and applications 82 (1994), S. 159-167 
    Details
    ISSN: 1573-2878
    Keywords: Alternative theorems ; quadratic forms
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract LetA 1 andA 2 be two symmetric matrices of ordern×n. According to Yuan, there exists a convex combination of these matrices which is positive semidefinite, if and only if the functionx∈R n ↦ max {x T A 1 x,x T A 2 x} is nonnegative. We study the case in which more than two matrices are involved. We study also a related question concerning the maximization of the minimum eigenvalue of a convex combination of symmetric matrices.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02191786
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    Paper (German National Licenses)
    Fulltext
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