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  • 1
    Electronic Resource
    Electronic Resource
    A projected lagrangian algorithm for semi-infinite programming (1985)
    Springer
    Mathematical programming 32 (1985), S. 337-356 
    Details
    ISSN: 1436-4646
    Keywords: Semi-Infinite Programming ; Descent Algorithm ; Penalty Function ; Lagrangian Function ; Global Convergence ; Second Order Convergence
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract A globally convergent algorithm is presented for the solution of a wide class of semi-infinite programming problems. The method is based on the solution of a sequence of equality constrained quadratic programming problems, and usually has a second order convergence rate. Numerical results illustrating the method are given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01582053
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  • 2
    Electronic Resource
    Electronic Resource
    An exact penalty function algorithm for semi-infinite programmes (1990)
    Springer
    BIT 30 (1990), S. 723-734 
    Details
    ISSN: 1572-9125
    Keywords: 65K05 ; 90C30
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract An algorithm for semi-inifinite programming using sequential quadratic programming techniques together with anL ∞ exact penalty function is presented, and global convergence is shown. An important feature of the convergence proof is that it does not require an implicit function theorem to be applicable to the semi-infinite constraints; a much weaker assumption concerning the finiteness of the number of global maximizers of each semi-infinite constraint is sufficient. In contrast to proofs based on an implicit function theorem, this result is also valid for a large class ofC 1 problems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01933219
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  • 3
    Electronic Resource
    Electronic Resource
    The rise and fall of the vector epsilon algorithm (1993)
    Springer
    Numerical algorithms 5 (1993), S. 275-286 
    Details
    ISSN: 1572-9265
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract The performance of the vector epsilon algorithm is governed by two important mathematical theorems which are briefly reviewed in context. We note that the performance of the vector epsilon algorithm is inevitably qualitatively incorrect for sequences whose generating functions have poles near unity. This difficulty is avoided by the use of hybrid vector Padé approximants.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02108462
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  • 4
    Electronic Resource
    Electronic Resource
    Some numerical experience with a globally convergent algorithm for nonlinearly constrained optimization (1980)
    Springer
    Journal of optimization theory and applications 32 (1980), S. 1-16 
    Details
    ISSN: 1573-2878
    Keywords: Nonlinear programming ; global convergence ; numerical experience
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Global convergence properties are established for a quite general form of algorithms for solving nonlinearly constrained minimization problems. A useful feature of the methods considered is that they can be implemented easily either with or without using quadratic programming techniques. A particular implementation, designed to be both efficient and robust, is described in detail. Numerical results are presented and discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00934840
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  • 5
    Electronic Resource
    Electronic Resource
    A two-parameter exact penalty function for nonlinear programming (1994)
    Springer
    Journal of optimization theory and applications 83 (1994), S. 49-61 
    Details
    ISSN: 1573-2878
    Keywords: Nonlinear optimization ; exact penalty functions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A sequential quadratic programming algorithm for nonlinear programs using anl ∞-exact penalty function is described. Numerical results are also presented. These results show that the algorithm is competitive with other exact penalty function based algorithms and that the inclusion of the second penalty parameter can be advantageous.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02191761
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  • 6
    Electronic Resource
    Electronic Resource
    Numerical experiments in semi-infinite programming (1996)
    Springer
    Computational optimization and applications 6 (1996), S. 169-189 
    Details
    ISSN: 1573-2894
    Keywords: semi-infinite programming ; nonlinear optimisation ; L ∞ exact penalty function
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract A quasi-Newton algorithm for semi-infinite programming using an L ∞ exact penalty function is described, and numerical results are presented. Comparisons with three Newton algorithms and one other quasi-Newton algorithm show that the algorithm is very promising in practice.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00249645
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  • 7
    Electronic Resource
    Electronic Resource
    Frame Based Methods for Unconstrained Optimization (2000)
    Springer
    Journal of optimization theory and applications 107 (2000), S. 261-274 
    Details
    ISSN: 1573-2878
    Keywords: derivative free optimization ; positive basis methods ; convergence analysis ; frame based methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper describes a wide class of direct search methods for unconstrained optimization, which make use of fragments of grids called frames. Convergence is shown under mild conditions which allow successive frames to be rotated, translated, and scaled relative to one another.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1026429319405
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  • 8
    Electronic Resource
    Electronic Resource
    Circle fitting by linear and nonlinear least squares (1993)
    Springer
    Journal of optimization theory and applications 76 (1993), S. 381-388 
    Details
    ISSN: 1573-2878
    Keywords: Curve fitting ; circle fitting ; total least squares ; nonlinear least squares
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The problem of determining the circle of best fit to a set of points in the plane (or the obvious generalization ton-dimensions) is easily formulated as a nonlinear total least-squares problem which may be solved using a Gauss-Newton minimization algorithm. This straight-forward approach is shown to be inefficient and extremely sensitive to the presence of outliers. An alternative formulation allows the problem to be reduced to a linear least squares problem which is trivially solved. The recommended approach is shown to have the added advantage of being much less sensitive to outliers than the nonlinear least squares approach.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00939613
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  • 9
    Electronic Resource
    Electronic Resource
    On the calculation of minimum variance estimators for unobservable dependent variables (1993)
    Springer
    Computational optimization and applications 2 (1993), S. 337-341 
    Details
    ISSN: 1573-2894
    Keywords: Minimum variance estimators ; regression ; unobservable dependency ; Sylvester's law of inertia
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract The determination of minimum variance estimators in an unusual context is considered. The problem arises from an attempt to perform a regression with an unobservable dependent variable. The required minimum variance estimator is shown to satisfy a linear system of equations where the coefficient matrix has a simple structure. Uniqueness of the estimator is established by determining necessary and sufficient conditions on the data which guarantee positive definiteness of this coefficient matrix. Numerical aspects of the method of computation are also briefly explored.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01299545
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  • 10
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    A two-parameter exact penalty function for nonlinear programming (1994)
    Springer
    Details
    Publication Date: 1994-10-01
    Print ISSN: 0022-3239
    Electronic ISSN: 1573-2878
    Topics: Mathematics
    Published by Springer
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