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  • Mathematics  (7)
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  • Mathematics  (7)
  • 1
    Electronic Resource
    Electronic Resource
    Duality for a class of quasiconvex programs (1983)
    Springer
    Journal of optimization theory and applications 40 (1983), S. 515-536 
    Details
    ISSN: 1573-2878
    Keywords: Fractional programming ; duality ; quasiconvex functions ; pseudoduality ; stationary points
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper derives a duality relation between a pair of explicitly quasiconvex and quasiconcave programs.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00933969
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  • 2
    Electronic Resource
    Electronic Resource
    Spatial and time decomposition algorithms for dynamic nonlinear network optimization using duality (1984)
    Springer
    Journal of optimization theory and applications 42 (1984), S. 77-101 
    Details
    ISSN: 1573-2878
    Keywords: Dynamic optimization ; duality ; decomposition ; distribution networks ; multilevel optimization
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The structural and computational aspects of two decomposition algorithms suitable for dynamic optimization of nonlinear interconnected networks are examined. Both methods arise from a decomposition based on Lagrangian duality theory of the addressed dynamic optimization problem, which is the minimization of energy costs over a given time period, subject to the requirement that the network equations and inequality restrictions are satisfied. The first algorithm uses a spatial decomposition of the state space into subgroups of state variables associated with particular network zones. This leads to a number of lower-dimensional optimization problems which can be solved individually at one level and coordinated at a higher level to account for interactions between these zones. The second algorithm uses time decomposition to solve a sequence of static optimization problems, one for each time increment into which the interval is subdivided, which are then coordinated to take account of dynamic interaction between the time increments. Computational results from an actual network in the United Kingdom are presented for both methods.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00934134
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  • 3
    Electronic Resource
    Electronic Resource
    Theorems of the alternative and optimality conditions (1984)
    Springer
    Journal of optimization theory and applications 42 (1984), S. 331-365 
    Details
    ISSN: 1573-2878
    Keywords: Theorems of the alternative ; optimality conditions ; regularity conditions ; constraints qualification ; separation theorems ; Lagrangian functions ; penalty functions ; duality
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A theorem of the alternative is stated for generalized systems. It is shown how to deduce, from such a theorem, known optimality conditions like saddle-point conditions, regularity conditions, known theorems of the alternative, and new ones. Exterior and interior penalty approaches, weak and strong duality are viewed as weak and strong alternative, respectively.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00935321
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  • 4
    Electronic Resource
    Electronic Resource
    Duality in generalized fractional programming via Farkas' lemma (1983)
    Springer
    Journal of optimization theory and applications 41 (1983), S. 417-424 
    Details
    ISSN: 1573-2878
    Keywords: Fractional programming ; nonconvex programming ; duality ; Farkas' lemma
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract For fractional programs involving several ratios in the objective function, a dual is introduced with the help of Farkas' lemma. Often the dual is again a generalized fractional program. Duality relations are established under weak assumptions. This is done in both the linear case and the nonlinear case. We show that duality can be obtained for these nonconvex programs using only a basic result on linear (convex) inequalities.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00935361
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  • 5
    Electronic Resource
    Electronic Resource
    Optimality conditions and strong duality in abstract and continuous-time linear programming (1983)
    Springer
    Journal of optimization theory and applications 40 (1983), S. 61-76 
    Details
    ISSN: 1573-2878
    Keywords: Optimality ; duality ; infinite-dimensional linear programs ; positive extendability ; linear functionals ; continuous time linear programs ; generalized duality ; functional analysis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this work, optimality conditions for infinite-dimensional linear programs are considered. Strong duality as an optimality condition is investigated. A new approach to duality in the form of positive extendability of linear functionals is proposed. A necessary and sufficient condition for duality in the form of a boundedness test of a related linear program is developed. Elaborating on the continuous time framework, counter cases where duality is not valid are given. In lieu of duality, other generalized duality conditions are proposed for the purpose of testing the optimality of a solution.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00934631
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  • 6
    Electronic Resource
    Electronic Resource
    About isermann duality (1983)
    Springer
    Journal of optimization theory and applications 41 (1983), S. 481-490 
    Details
    ISSN: 1573-2878
    Keywords: Linear programming ; multiple objectives ; duality
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this note, we consider the following multiple-objective linear program: maxCx, such thatAx=b,x≧0, and its associated Isermann dual program: minUb, such thatUAW≤Cw, for now≧0. We give a simple proof of the known fact that, for every dual efficient pointU°, there is a primal efficient pointx°, such thatU°b=Cx°. Parts of the ingredients in this proof are useful in exploring the structure of the dual feasible set of function values {Ub¦UAw≤Cw, for now≧0}.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00935367
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  • 7
    Electronic Resource
    Electronic Resource
    On the multiplicative properties of the de Rham—Witt complex. I (1984)
    Springer
    Arkiv för matematik 22 (1984), S. 185-239 
    Details
    ISSN: 1871-2487
    Keywords: Crystalline cohomology ; de Rham—Witt complex ; duality ; Kunneth formulas
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Due to the length this work is published in two parts. The second part will appear in Vol 23: 1 of this journal. Part 1 has the subtitle “Duality for the de Rham—Witt complex” and Part 2 is entitled “A Künneth formula for the Hodge—Witt complex”.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02384380
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