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  • 1
    Electronic Resource
    Electronic Resource
    On unbounded solutions of Bellman's equation associated with optimal switching control problems with state constraints (1995)
    Springer
    Applied mathematics & optimization 31 (1995), S. 1-17 
    Details
    ISSN: 1432-0606
    Keywords: Bellman equation ; Hamilton-Jacobi equation ; Quasi-variational inequality ; Viscosity solution ; Unbounded solutions ; Optimal switching ; Optimal control ; State constraints ; Production engineering ; 49C05 ; 49C20 ; 49B10 ; 49A36
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We study a quasi-variational inequality system with unbounded solutions. It represents the Bellman equation associated with an optimal switching control problem with state constraints arising from production engineering. We show that the optimal cost is the unique viscosity solution of the system.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01182554
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Global optimization of arborescent multilevel inventory systems (1995)
    Springer
    Journal of global optimization 6 (1995), S. 269-292 
    Details
    ISSN: 1573-2916
    Keywords: Global optimization ; inventory problems ; discrete Hamilton-Jacobi-Bellman equations ; quasi-variational inequalities ; subsolutions and supersolutions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We consider the numerical resolution of hierarchical inventory problems under global optimization. First we describe the model as well as the dynamical stochastic system and the impulse controls involved. Next we characterize the optimal cost function and we formulate the Hamilton-Jacobi-Bellman equations. We present a numerical scheme and a fast algorithm of resolution, with a result on the speed of convergence. Finally, we apply the discretization method to some examples where we show the usefulness of the proposed numerical method as well as the advantages of operating under global optimization.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01099465
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Variational approach to serial multilevel production/inventory systems (1990)
    Springer
    Journal of optimization theory and applications 65 (1990), S. 447-483 
    Details
    ISSN: 1573-2878
    Keywords: Stochastic control ; quasi-variational inequalities ; hierarchical production/inventory systems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We discuss stochastic, continuous-time models of serial multilevel production/inventory systems using quasi-variational inequalities. The value functions are characterized as maximum solutions of suitable equivalent problems. Then, we show how to construct optimal centralized policies and, if possible, decentralized policies. Finally, we present some numerical examples for the deterministic case.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00939561
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    Paper (German National Licenses)
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