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  • mathematical programming  (3)
  • Springer  (3)
  • American Geophysical Union (AGU)
  • 1975-1979  (3)
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  • Springer  (3)
  • American Geophysical Union (AGU)
Years
  • 1975-1979  (3)
Year
  • 1
    Electronic Resource
    Electronic Resource
    An accelerated multiplier method for nonlinear programming (1977)
    Springer
    Journal of optimization theory and applications 21 (1977), S. 137-174 
    Details
    ISSN: 1573-2878
    Keywords: Augmented penalty function ; method of multipliers ; penalty function methods ; nonlinear programming ; mathematical programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper describes an accelerated multiplier method for solving the general nonlinear programming problem. The algorithm poses a sequence of unconstrained optimization problems. The unconstrained problems are solved using a rank-one recursive algorithm described in an earlier paper. Multiplier estimates are obtained by minimizing the error in the Kuhn-Tucker conditions using a quadratic programming algorithm. The convergence of the sequence of unconstrained problems is accelerated by using a Newton-Raphson extrapolation process. The numerical effectiveness of the algorithm is demonstrated on a relatively large set of test problems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00932517
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Solving the nonlinear least square problem: Application of a general method (1976)
    Springer
    Journal of optimization theory and applications 18 (1976), S. 469-483 
    Details
    ISSN: 1573-2878
    Keywords: Nonlinear least-square problems ; parameter optimization ; penalty function methods ; mathematical programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract An algorithm for solving the general nonlinear least-square problem is developed. An estimate for the Hessian matrix is constructed as the sum of two matrices. The first matrix is the usual first-order estimate used by the Gauss method, while the second matrix is generated recursively using a rank-one formula. Test results indicate that the method is superior to the standard Gauss method and compares favorably with other methods, especially for problems with nonzero residuals at the solution.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00932656
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  • 3
    Electronic Resource
    Electronic Resource
    An improved penalty function method for solving constrained parameter optimization problems (1975)
    Springer
    Journal of optimization theory and applications 16 (1975), S. 1-24 
    Details
    ISSN: 1573-2878
    Keywords: Penalty-function methods ; mathematical programming ; nonlinear programming ; pseudo Newton-Raphson methods ; parameter optimization
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract An effective algorithm is described for solving the general constrained parameter optimization problem. The method is quasi-second-order and requires only function and gradient information. An exterior point penalty function method is used to transform the constrained problem into a sequence of unconstrained problems. The penalty weightr is chosen as a function of the pointx such that the sequence of optimization problems is computationally easy. A rank-one optimization algorithm is developed that takes advantage of the special properties of the augmented performance index. The optimization algorithm accounts for the usual difficulties associated with discontinuous second derivatives of the augmented index. Finite convergence is exhibited for a quadratic performance index with linear constraints; accelerated convergence is demonstrated for nonquadratic indices and nonlinear constraints. A computer program has been written to implement the algorithm and its performance is illustrated in fourteen test problems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00935620
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