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  • 1
    Electronic Resource
    Electronic Resource
    Unification of basic and composite nondifferentiable optimization (1995)
    Springer
    Mathematical programming 70 (1995), S. 233-249 
    Details
    ISSN: 1436-4646
    Keywords: Nondifferentiable optimization ; Composite NDO ; Basic NDO ; Second-order convergence ; Global convergence ; Polyhedral approximation ; Convex programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract There are two main classes of iterative methods in nondifferentiable optimization (NDO). In thebasic NDO, the information is limited to the objective function and at least one element of its subdifferential, while in thecomposite NDO, the objective function is split into a sum of a smooth and a nonsmooth function. Our work unifies these two approaches for benefiting of their respective advantages.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01585939
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    A two parameter mixed interior-exterior penalty algorithm (1995)
    Springer
    Mathematical methods of operations research 41 (1995), S. 25-55 
    Details
    ISSN: 1432-5217
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract In this paper, we analyze the mixed penalty methods introduced in the classic book of Fiacco and McCormick usingtwo distinct penalty parametersr, t. The two penalty coefficients induce a two-parameter differentiable trajectory. We analyze the numerical behaviour of an extrapolation strategy that follows the path of the two-parameter trajectory. We show also how to remove the ill-conditioning by suitable transformations of the equations. In the resulting theory, we show that function values as well as distances to the optimum are both governed by the same behaviour as interior methods (two-step superlinearly convergent, with limiting exponent 4/3).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01415063
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Combining the Stochastic Counterpart and Stochastic Approximation Methods (1997)
    Springer
    Discrete event dynamic systems 7 (1997), S. 5-28 
    Details
    ISSN: 1573-7594
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this work, we examine how to combine the score function method with the standard crude Monte Carlo and experimental design approaches, in order to evaluate the expected performance of a discrete event system and its associated gradient simultaneously for different scenarios (combinations of parameter values), as well as to optimize the expected performance with respect to two parameter sets, which represent parameters of the underlying probability law (for the systems evolution) and parameters of the sample performance measure, respectively. We explore how the stochastic approximation and stochastic counterpart methods can be combined to perform optimization with respect to both sets of parameters at the same time. We outline three combined algorithms of that form, one sequential and two parallel, and give a convergence proof for one of them. We discuss a number of issues related to the implementation and convergence of those algorithms, introduce averaging variants, and give numerical illustrations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008286324509
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    Paper (German National Licenses)
    Fulltext
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