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  • 1
    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.
    Type of Medium: Electronic Resource
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  • 2
    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.
    Type of Medium: Electronic Resource
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  • 3
    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.
    Type of Medium: Electronic Resource
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  • 4
    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.
    Type of Medium: Electronic Resource
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  • 5
    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.
    Type of Medium: Electronic Resource
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