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  • Articles  (5)
  • Nonlinear Programming  (5)
  • Springer  (5)
  • American Chemical Society
  • Annual Reviews
  • Blackwell Publishing Ltd
  • Elsevier
  • Wiley
  • 2005-2009
  • 1990-1994
  • 1980-1984  (5)
  • 2008
  • 1982  (5)
  • Mathematics  (5)
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  • Articles  (5)
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  • Springer  (5)
  • American Chemical Society
  • Annual Reviews
  • Blackwell Publishing Ltd
  • Elsevier
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  • 2005-2009
  • 1990-1994
  • 1980-1984  (5)
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  • 1
    Electronic Resource
    Electronic Resource
    On the computational utility of posynomial geometric programming solution methods (1982)
    Springer
    Mathematical programming 22 (1982), S. 163-201 
    Details
    ISSN: 1436-4646
    Keywords: Geometric Programming ; Code Comparisons ; Numerical Testing ; Nonlinear Programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Ten codes or code variants were used to solve the five equivalent posynomial GP problem formulations. Four of these codes were general NLP codes; six were specialized GP codes. A total of forty-two test problems was solved with up to twenty randomly generated starting points per problem. The convex primal formulation is shown to be intrinsically easiest to solve. The general purpose GRG code called OPT appears to be the most efficient code for GP problem solution. The reputed superiority of the specialized GP codes GGP and GPKTC appears to be largely due to the fact that these codes solve the convex primal formulation. The dual approaches are only likely to be competitive for small degree of difficulty, tightly constrained problems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01581036
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  • 2
    Electronic Resource
    Electronic Resource
    A globally convergent constrained quasi-Newton method with an augmented lagrangian type penalty function (1982)
    Springer
    Mathematical programming 23 (1982), S. 75-86 
    Details
    ISSN: 1436-4646
    Keywords: Constrained Optimization ; Global Convergence ; Nonlinear Programming ; Penalty Function ; Quasi-Newton Method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract The recently proposed quasi-Newton method for constrained optimization has very attractive local convergence properties. To force global convergnce of the method, a descent method which uses Zangwill's penalty function and an exact line search has been proposed by Han. In this paper a new method which adopts a differentiable penalty function and an approximate line is presented. The proposed penalty function has the form of the augmented Lagrangian function. An algorithm for updating parameters which appear in the penalty function is described. Global convergence of the given method is proved.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01583780
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  • 3
    Electronic Resource
    Electronic Resource
    On optimality conditions for structured families of nonlinear programming problems (1982)
    Springer
    Mathematical programming 22 (1982), S. 82-92 
    Details
    ISSN: 1436-4646
    Keywords: Generic Programming ; Optimality Conditions ; Nonlinear Programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Optimality conditions for families of nonlinear programming problems inR n are studied from a generic point of view. The objective function and some of the constraints are assumed to depend on a parameter, while others are held fixed. Techniques of differential topology are used to show that under suitable conditions, certain strong second-order conditions are necessary for optimality except possibly for parameter values lying in a negligible set.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01581027
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  • 4
    Electronic Resource
    Electronic Resource
    Nonlinear programming via an exact penalty function: Global analysis (1982)
    Springer
    Mathematical programming 24 (1982), S. 137-161 
    Details
    ISSN: 1436-4646
    Keywords: Nonlinear Programming ; Exact Penalty Methods ; Successive Quadratic Programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract In this paper we motivate and describe an algorithm to solve the nonlinear programming problem. The method is based on an exact penalty function and possesses both global and superlinear convergence properties. We establish the global qualities here (the superlinear nature is proven in [7]). The numerical implementation techniques are briefly discussed and preliminary numerical results are given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01585101
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  • 5
    Electronic Resource
    Electronic Resource
    Nonlinear programming via an exact penalty function: Asymptotic analysis (1982)
    Springer
    Mathematical programming 24 (1982), S. 123-136 
    Details
    ISSN: 1436-4646
    Keywords: Nonlinear Programming ; Exact Penalty Methods ; Successive Quadratic Programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract In this paper we consider the final stage of a ‘global’ method to solve the nonlinear programming problem. We prove 2-step superlinear convergence. In the process of analyzing this asymptotic behavior, we compare our method (theoretically) to the popular successive quadratic programming approach.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01585100
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