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  • 1
    Electronic Resource
    Electronic Resource
    A Farkas lemma for difference sublinear systems and quasidifferentiable programming (1994)
    Springer
    Mathematical programming 63 (1994), S. 109-125 
    Details
    ISSN: 1436-4646
    Keywords: Alternative theorems ; quasidifferentiable programming ; nonsmooth analysis ; optimality conditions ; difference convex programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract A new generalized Farkas theorem of the alternative is presented for systems involving functions which can be expressed as the difference of sublinear functions. Various other forms of theorems of the alternative are also given using quasidifferential calculus. Comprehensive optimality conditions are then developed for broad classes of infinite dimensional quasidifferentiable programming problems. Applications to difference convex programming and infinitely constrained concave minimization problems are also discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01582061
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  • 2
    Electronic Resource
    Electronic Resource
    The theorem of the alternative, the key-theorem, and the vector-maximum problem (1975)
    Springer
    Mathematical programming 8 (1975), S. 332-344 
    Details
    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Consequences of a general formulation of the theorem of the alternative are exploited.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01580450
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  • 3
    Electronic Resource
    Electronic Resource
    An iterative method, having linear rate of convergence, for solving a pair of dual linear programs (1972)
    Springer
    Mathematical programming 3 (1972), S. 302-311 
    Details
    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract An iterative method for dual linear programming problems is described, and its rate of convergence is established.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01585003
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    Compatibility of approximate solution of linear equations with given error bounds for coefficients and right-hand sides (1964)
    Springer
    Numerische Mathematik 6 (1964), S. 405-409 
    Details
    ISSN: 0945-3245
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In the spirit ofWilkinson's [1, 2] backward error analysis, conditions are established under which a given approximate solution of a system ofn linear equations withn unknowns is the exact solution of a modified system whose coefficients and right-hand sides are within a given neighborhood of those of the original system.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01386090
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    Paper (German National Licenses)
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  • 5
    Electronic Resource
    Electronic Resource
    Time-Dependent Traffic Equilibria (1999)
    Springer
    Journal of optimization theory and applications 103 (1999), S. 543-555 
    Details
    ISSN: 1573-2878
    Keywords: Transportation networks ; equilibrium solutions ; Wardrop condition ; time-dependent requirements
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We consider the existence, characterization, and calculation of equilibria in transportation networks, when the route capacities and demand requirements depend on time. The problem is situated in a Banach space setting and formulated in terms of a variational inequality.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1021779823196
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  • 6
    Electronic Resource
    Electronic Resource
    An example of a bad quasicomplementarity problem (1996)
    Springer
    Journal of optimization theory and applications 90 (1996), S. 213-215 
    Details
    ISSN: 1573-2878
    Keywords: Quasicomplementarity problems ; unbounded solution set ; homogeneous mappings
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract An example is given of a parametric, nonlinear quasicomplementarity problem having the property that, for every value of the parameters, the solution set is nonempty and unbounded.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02192254
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  • 7
    Electronic Resource
    Electronic Resource
    Mathematical programs with a two-dimensional reverse convex constraint (1991)
    Springer
    Journal of global optimization 1 (1991), S. 145-154 
    Details
    ISSN: 1573-2916
    Keywords: Reverse convex program ; global optimization
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We consider the problem min {f(x): x ∈ G, T(x) ∉ int D}, where f is a lower semicontinuous function, G a compact, nonempty set in ℝn, D a closed convex set in ℝ2 with nonempty interior and T a continuous mapping from ℝn to ℝ2. The constraint T(x) ∉ int D is a reverse convex constraint, so the feasible domain may be disconnected even when f, T are affine and G is a polytope. We show that this problem can be reduced to a quasiconcave minimization problem over a compact convex set in ℝ2 and hence can be solved effectively provided f, T are convex and G is convex or discrete. In particular we discuss a reverse convex constraint of the form 〈c, x〉 · 〈d, x〉≤1. We also compare the approach in this paper with the parametric approach.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00119988
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  • 8
    Electronic Resource
    Electronic Resource
    Flow in networks with amplification and coupling (1966)
    Springer
    Mathematical methods of operations research 10 (1966), S. 42-49 
    Details
    ISSN: 1432-5217
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Description / Table of Contents: Summary The network model presented in an earlier paper [1] is generalized by introducing amplification in arcs and coupling between arcs. The appropriate modifications of the earlier results are stated and the usefulness of the new model is illustrated by examples.
    Notes: Zusammenfassung Das in einer früheren Arbeit [1] angegebene Netzwerkmodell wird durch Einführung von Verstärkern in Leitungszweigen und Kopplung von Leitungszweigen verallgemeinert. Die entsprechenden Verallgemeinerungen der früheren Ergebnisse werden besprochen, und die Nützlichkeit des neuen Modells wird durch Beispiele illustriert.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01918283
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    Paper (German National Licenses)
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  • 9
    Electronic Resource
    Electronic Resource
    Eine allgemeine, symmetrische Formulierung des Dekompositionsprinzips für duale Paare nichtlinearer Minmax- und Maxmin-Probleme (1974)
    Springer
    Mathematical methods of operations research 18 (1974), S. 1-18 
    Details
    ISSN: 1432-5217
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Description / Table of Contents: Summary A general formulation of decomposition methods for finding saddle-points of convexconcave functions is proposed.
    Notes: Zusammenfassung Es wird eine allgemeine Formulierung des Dekompositionsverfahrens zur Lösung konvex-konkaver Sattelpunktprobleme angegeben.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01949709
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  • 10
    Electronic Resource
    Electronic Resource
    Characterization of weakly efficient points (1988)
    Springer
    Mathematical methods of operations research 32 (1988), S. 375-393 
    Details
    ISSN: 1432-5217
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Description / Table of Contents: Zusammenfassung Es werden schwach effiziente Punkte einer AbbildungF: S → Y charakterisiert, wobei der zulässige BereichS durch unendlich viele Restriktionen bestimmt wird undY mit einem beliebigen konvexen Ordnungskegel versehen ist. Im linearen und im konvexen Fall wird eine notwendige und hinreichende Bedingung angegeben, die keine Regularitätsvoraussetzung benötigt.
    Notes: Abstract Weakly efficient points of a mappingF: S → Y are characterized, where the feasible setS is given by infinitely many constraints, andY is equipped with an arbitrary convex ordering. In the linear and in the convex case a necessary and sufficient condition is given, which needs no constraint qualification.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01920037
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