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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
    ISSN: 1432-5217
    Keywords: Key words: Combinatorial optimization ; complexity ; ℳ?-completeness ; scheduling ; assignment ; stack
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract. In this note, we prove ??-completeness of the following problem: Given a set of trams of different types, which are stacked on sidings in their depot and an order in which trams of specified types are supposed to leave. Is there an assignment of trams to departure times without any shunting movements? In the particular case where the number of sidings is fixed, the problem is solvable in polynomial time. We derive a dynamic program and improve its performance by a state elimination scheme. We implemented three variants of the dynamic program and applied them to random data as well as to real-world data.
    Type of Medium: Electronic Resource
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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: flow shop ; permutation schedules ; complexity ; approximation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract In this paper, we study two versions of the two machine flow shop scheduling problem, where schedule length is to be minimized. First, we consider the two machine flow shop with setup, processing, and removal times separated. It is shown that an optimal solution need not be a permutation schedule, and that the problem isNP-hard in the strong sense, which contradicts some known results. The tight worst-case bound for an optimal permutation solution in proportion to a global optimal solution is shown to be 3/2. An O(n) approximation algorithm with this bound is presented. Secondly, we consider the two machine flow shop with finite storage capacity. Again, it is shown that there may not exist an optimal solution that is a permutation schedule, and that the problem isNP-hard in the strong sense.
    Type of Medium: Electronic Resource
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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.
    Type of Medium: Electronic Resource
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  • 7
    ISSN: 1432-5217
    Keywords: 0–1 programming ; surrogate constraints ; surrogate dual ; ellipsoid algorithm ; complexity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Description / Table of Contents: Zusammenfassung Es wird gezeigt, daß das “surrogate duale” Problem zu einer linearen Optimierungsaufgabe mit binären Variablen durch 0(m 3) Rucksackprobleme gelöst werden kann. Dabei bezeichnetm die Anzahl der Nebenbedingungen.
    Notes: Abstract It is shown that the surrogate dual of a 0–1 programming problem can be solved by 0(m 3) knapsack calls, ifm denotes the number of constraints.
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  • 8
    ISSN: 1432-5217
    Keywords: graph algorithms ; matching ; complexity ; succinct presentation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Description / Table of Contents: Zusammenfassung Es wird die Komplexität von Graphenproblemen untersucht, wenn die Graphen alsVertex-Multiplicity-Graphen gegeben sind. Bei dieser Darstellung kann eine unabhängige Menge von Knoten, die mit allen anderen Knoten des Graphen in der gleichen Weise verbunden ist, durch einen Knoten und die Größe der unabhängigen Menge (in Binärdarstellung) gegeben werden. Wenn man diese Darstellung verwendet, so kann man erwarten, daß die Komplexität der Graphenprobleme höchstens exponentiell wächst. In der Tat wird gezeigt, daß die RNC-Probleme UNARY NETWORK FLOW und PERFECT MATCHINGP-vollständig werden, daß die NP-vollständigen Probleme CHLIQUE, MAXIMUM INDEPENDENT SET und CHROMATIC NUMBER NP-vollständig bleiben und daß das eineP-vollständige Variante des Problems CIRCUIT VALUE PSPACE-vollständig wird.
    Notes: Abstract The complexity of graph problems is investigated when the graphs are presented asvertex multiplicity graphs. In this presentation an independent set of vertices which are connected in the same way with the remaining vertices of the graph can be described by giving only one vertex and the size of the independent set in binary. Using this succinct graph presentation one can expect that the complexity of graph problems can blow up exponentially. In fact, it is shown that the RNC-problems UNARY NETWORK FLOW and PERFECT MATCHING becomeP-complete, that the NP-complete problems CHLIQUE, MAXIMUM INDEPENDENT SET and CHROMATIC NUMBER remain NP-complete and that aP-complete version of the CIRCUIT VALUE problem becomes PSPACE-complete.
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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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