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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    ISSN: 1432-5217
    Keywords: Loss Systems ; Output Processes ; Simulation ; Approximation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Description / Table of Contents: Zusammenfassung Für das BedienungsmodellG/G/1 ohne Warteraum wird eine Approximation des Abgangsprozesses im stationären Zustand angegeben, wobei allgemein verteilte Zwischenankunfts- und Bedienungszeiten angenommen sind. Ferner werden für den Fall, daß mehrere solche Bediener in Reihen geschaltet sind, approximative Resultate angegeben und mit Simulationen überprüft.
    Notes: Abstract The departure process from aG/G/1 loss system with generally distributed interarrival time, generally distributed service time, a single server, and no waiting room is approximated in steady state. Furthermore, the tandem behavior of the system is approximated, approximation results are provided, and are compared against those from a simulation study.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    ISSN: 1432-5217
    Keywords: Generalized convexity ; duality ; root term ; optimal solution
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract We extend the duality theorems for a class of nondifferentiable problems with Mond-Weir type duals.
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    ISSN: 1432-5217
    Keywords: Quasi-inverse ; epi-inverse ; hypo-inverse ; nondecreasing functions ; quasiconvex functions ; convex functions ; duality ; rearrangement ; modulus of continuity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Description / Table of Contents: Zusammenfassung In dieser Arbeit wird systematisch die Umkehrung monoton nichtfallender Funktionenf: ℝ → ℝ ∪ {−∞, +∞} studiert. Die Ergebnisse bilden die Grundlage für eine neue Dualitätstheorie quasikonvexer Probleme [6]. Da jedoch die Fragestellung bei einer ganzen Anzahl weiterer Situationen auftritt, verdient sie eine gesonderte Behandlung. Anwendungen in der Topologie, Wahrscheinlichkeitstheorie, monotonen Umordnungen und in der konvexen Analysis werden aufgezeigt und skizziert.
    Notes: Abstract This work is devoted to a systematic study of the inversion of nondecreasing one variable extended real-valued functions. Its results are preparatory for a new duality theory for quasiconvex problem [6]. However the question arises in a variety of situations and as such deserves a separate treatment. Applications to topology, probability theory, monotone rearrangements, convex analysis are either pointed out or sketched.
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    ISSN: 1432-5217
    Keywords: vectorial control-approximation problem ; vectorial location problem ; duality ; efficiency
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Description / Table of Contents: Zusammenfassung In der Arbeit werden für eine Klasse von vektoriellen Steuer-Approximationsproblemen in reellen reflexiven Banachräumen vektorielle Dualprobleme konstruiert und Dualitätseigenschaften hergeleitet. Als Spezialfall ergeben sich entsprechende Aussagen für vektorielle Standortprobleme.
    Notes: Abstract The author formulates vectorial dual problems for a certain class of vectorial control-approximation problems in real reflexive Banach spaces. A number of propositions concerning duality are derived. Corresponding propositions are mentioned for the special case of the vectorial location problems.
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  • 5
    ISSN: 1432-5217
    Keywords: Approximation ; Integration ; Sequential Stochastic Decision Process ; Discretization
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract We consider convex stochastic multistage problems and present an approximation technique which allows to analyse the error with respect to time. The technique is based on barycentric approximation of conditional and marginal probability spaces and requiresstrict nonanticipativity for the constraint multifunction and thesaddle property for the value functions.
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  • 6
    ISSN: 1432-5217
    Keywords: Markov decision processes ; countable state space ; Linear programming ; duality
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract We present an Linear Programming formulation of MDPs with countable state and action spaces and no unichain assumption. This is an extension of the Hordijk and Kallenberg (1979) formulation in finite state and action spaces. We provide sufficient conditions for both existence of optimal solutions to the primal LP program and absence of duality gap. Then, existence of a (possibly randomized) average optimal policy is also guaranteed. Existence of a stationary average optimal deterministic policy is also investigated.
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  • 7
    Electronic Resource
    Electronic Resource
    Springer
    ISSN: 1432-5217
    Keywords: Dynamic Programming ; Approximation ; Bounds ; Inventory model ; (s, S)-policies
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Description / Table of Contents: Zusammenfassung Es wird ein allgemeines dynamisches Optimierungsmodell mit endlichem Horizont betrachtet. Für verschiedene Näherungsverfahren für die minimalen erwarteten Gesamtkosten und die optimale Politik werden Schranken angegeben. Die Theorie wird sodann auf ein Lagerhaltungsmodell angewandt, um Schranken für „gute“ Bestellpolitiken zu erhalten.
    Notes: Summary We consider a general finite stage dynamic programming model. Bounds are derived for the approximation of the minimum expected total cost and of the optimal policy. The theory is applied to an inventory model to give bounds for “good” order policies.
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  • 8
    ISSN: 1432-5217
    Keywords: Network Flows ; Parametric Optimization ; Approximation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Description / Table of Contents: Zusammenfassung Wir betrachten maximale Flußprobleme, in denen die Kapazitäten lineare Funktionen eines Parameterst ∈ [0,T] sind. Da dieses Problem ein Spezialfall eines parametrischen linearen Programms ist, kann man den klassischen horizontalen Ansatz anwenden, mit dem optimale Lösungen sukzessive auf Teilintervallen von [0,T] bestimmt werden. Wir stellen einen alternativen Algorithmus vor, der in jeder Iteration die optimale Lösung für allet ∈ [0,T] approximiert. Dieser vertikalen Ansatz ist eine Art Markierungsalgorithmus, wobei die Flußvariablen stückweise lineare Funktionen sind. Flußvergrößerungen werden aufbedingten flußvergrößernden Wegen durchgeführt, die mittels modifizierter kürzester Wege Algorithmen gefunden werden können. Der vertikale Algorithmus kann sowohl zur Berechnung des optimalen parametrischen Flusses als auch zur Berechnung einer guten Approximation für allet benutzt werden, falls sich herausstellt, daß die Berechnung der optimalen Lösung zu zeitaufwendig ist.
    Notes: Abstract We consider the problem of finding maximal flows with respect to capacities which are linear functions of a parametert ∈ [0,T]. Since this problem is a special case of a parametric linear program the classichorizontal approach can be applied in which optimal solutions are computed for successive subintervals of [0,T]. We discuss an alternative algorithm which approximates in each iteration the optimal solution for allt ∈ [0,T]. Thisvertical algorithm is a labeling type algorithm where the flow variables are piecewise linear functions. Flow augmentations are done alongconditional flow augmenting paths which can be found by modified path algorithms. The vertical algorithm can be used to solve the parametric flow problem optimally as well as to compute a good approximation for allt if the computation of the optimal solution turns out to be too time consuming.
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  • 9
    Electronic Resource
    Electronic Resource
    Springer
    ISSN: 1432-5217
    Keywords: Optimization theory ; mathematical programming ; duality ; half spaces ; minimum norm duality ; separating hyperplanes
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract This note shows that half spaces play a very special role in the development of duality. In addition to the minimum norm duality, the duality in linear programming, and Wolfe's and Johri's formulations in nonlinear programming can all be derived via half spaces by following an identical five step procedure.
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