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  • 1
    Electronic Resource
    Electronic Resource
    Conjugate duality in generalized fractional programming (1989)
    Springer
    Journal of optimization theory and applications 60 (1989), S. 475-483 
    Details
    ISSN: 1573-2878
    Keywords: Conjugate functions ; convex analysis ; duality ; generalized fractional programs
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The concepts of conjugate duality are used to establish dual programs for a class of generalized nonlinear fractional programs. It is now known that, under certain restrictions, a symmetric duality exists for generalized linear fractional programs. In this paper, we establish this symmetric duality for the nonlinear case.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00940349
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  • 2
    Electronic Resource
    Electronic Resource
    Generalized geometric programming applied to problems of optimal control: Part I, theory (1980)
    Springer
    Journal of optimization theory and applications 30 (1980), S. 149-149 
    Details
    ISSN: 1573-2878
    Keywords: Generalized geometric programming ; control theory ; convex analysis ; duality
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A modification to the formulation in Ref. 1 is given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00934597
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  • 3
    Electronic Resource
    Electronic Resource
    Composite geometric programming (1990)
    Springer
    Journal of optimization theory and applications 64 (1990), S. 101-118 
    Details
    ISSN: 1573-2878
    Keywords: Geometric programming ; convex programming ; exponential geometric programming ; transcendental geometric programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Geometric programming is based on functions called posynomials, the terms of which are log-linear. This class of programs is extended from the composition of an exponential and a linear function to an exponential and a convex function. The resulting duality theory for composite geometric programs retains many of the qualities of geometric programming duality, while at the same time encompassing new areas of application. As an application, composite geometric programming is applied to exponential geometric programming. A pure dual is developed for the first time and used to solve a problem from the literature.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00940025
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    Convex dual for quadratic concave fractional programs (1996)
    Springer
    Journal of optimization theory and applications 91 (1996), S. 115-122 
    Details
    ISSN: 1573-2878
    Keywords: Convex dual ; quadratic-concave fractional programs ; conjugate duality
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract For a fractional program with a quadratic numerator and an arbitrary concave denominator, a new convex dual program is derived. Concepts of conjugate duality are used to obtain an explicit representation of the dual.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02192285
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    Paper (German National Licenses)
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  • 5
    Electronic Resource
    Electronic Resource
    Duality of a Nonconvex Sum of Ratios (1998)
    Springer
    Journal of optimization theory and applications 98 (1998), S. 151-159 
    Details
    ISSN: 1573-2878
    Keywords: Fractional programs ; sum of ratios ; geometric programs ; reversed constraints
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract For mathematical programs with objective involving a sum of ratios of affine functions, there are few theoretical results due to the nonconvex nature of the program. In this paper, we derive a duality theory for these programs by establishing their connection with geometric programming. This connection allows one to bring to bear the powerful theory and computational algorithms associated with geometric programming.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1022693032053
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    Paper (German National Licenses)
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  • 6
    Electronic Resource
    Electronic Resource
    Optimal regulation of the service rate for a queue with finite waiting space (1976)
    Springer
    Journal of optimization theory and applications 20 (1976), S. 245-250 
    Details
    ISSN: 1573-2878
    Keywords: Queueing ; control theory ; singular control ; steady state
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The optimal control for the service rate of a single-server queue with limited waiting space is derived. Costs are associated with providing the service and with waiting. A comparison with the traditional steady-state result is made.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01767454
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  • 7
    Electronic Resource
    Electronic Resource
    Generalized geometric programming applied to problems of optimal control: I. Theory (1978)
    Springer
    Journal of optimization theory and applications 26 (1978), S. 117-129 
    Details
    ISSN: 1573-2878
    Keywords: Generalized geometric programming ; control theory ; convex analysis ; duality
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The interest in convexity in optimal control and the calculus of variations has gone through a revival in the past decade. In this paper, we extend the theory of generalized geometric programming to infinite dimensions in order to derive a dual problem for the convex optimal control problem. This approach transfers explicit constraints in the primal problem to the dual objective functional.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00933274
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    Paper (German National Licenses)
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  • 8
    Electronic Resource
    Electronic Resource
    On the optimal control of a single-server queueing system: Reply (1978)
    Springer
    Journal of optimization theory and applications 26 (1978), S. 463-464 
    Details
    ISSN: 1573-2878
    Keywords: Optimal control ; queueing systems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This comment replies to a criticism due to Klein and Gruver (Ref. 1) of our earlier paper (Ref. 2) on the application of control theory to a queueing system. The criticism concerns the state-space diagram and the table which we inadvertently gave for the terminal-reward problem, albeit incorrectly labeled, rather than for the free-endpoint problem considered in our paper. We show that the solution given by Klein and Gruver is itself incorrect and nonoptimal.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00933467
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    Paper (German National Licenses)
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  • 9
    Electronic Resource
    Electronic Resource
    A Duality Theory for a Class of Generalized Fractional Programs (1998)
    Springer
    Journal of global optimization 12 (1998), S. 239-245 
    Details
    ISSN: 1573-2916
    Keywords: Fractional program ; Multi-ratios ; Conjugate duality ; Convexity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In generalized fractional programming, one seeks to minimize the maximum of a finite number of ratios. Such programs are, in general, nonconvex and consequently are difficult to solve. Here, we consider a particular case in which the ratio is the quotient of a quadratic form and a positive concave function. The dual of such a problem is constructed and a numerical example is given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008274708071
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  • 10
    Electronic Resource
    Electronic Resource
    The analysis of risky portfolios by geometric programming (1979)
    Springer
    Mathematical methods of operations research 23 (1979), S. 207-217 
    Details
    ISSN: 1432-5217
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Description / Table of Contents: Zusammenfassung Ausgangspunkt dieses Aufsatzes ist das folgende Portfolio-Problem: Ein gegebenes Budget ist auf verschiedene Anlagemöglichkeiten so aufzuteilen, daß dabei der erwartete Nutzen des Gesamtertrages maximiert wird. Dieses Problem wird — zunächst ohne Verwendung einer Wahrscheinlichkeitsverteilung für die Erträge der einzelnen Anlagemöglichkeiten — mit Hilfe der verallgemeinerten geometrischen Programmierung analysiert. Es werden duale Programme abgeleitet, die die Lösung des Portfolio-Problems für verschiedene spezielle Verteilungsfunktionen in sehr einfacher Weise gestatten.
    Notes: Summary The problem of selecting a portfolio from a set of risky business ventures is considered. It is formulated as a maximization of the risk-adjusted (certainty-equivalent) profit for the portfolio based upon the exponential utility function and analysed via generalised geometric programming. Generalised geometric programming provides dual programs for the general case and for particular probability distributions. The particular cases of gamma, binomial, and normal distributions are converted into duals which arc of one dimension regardless of the number of portfolios.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01919485
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