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  • duality  (3)
  • Fractional program  (1)
  • Geometric programming  (1)
  • 1
    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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  • 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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  • 4
    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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  • 5
    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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