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  • Articles  (134)
  • Other Sources
  • CR: 5.17  (97)
  • Nonlinear programming  (37)
  • 1985-1989  (25)
  • 1980-1984  (109)
  • Mathematics  (134)
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  • Books  (1)
  • Articles  (134)
  • Other Sources
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  • 1
    Electronic Resource
    Electronic Resource
    NLPQL: A fortran subroutine solving constrained nonlinear programming problems (1986)
    Springer
    Annals of operations research 5 (1986), S. 485-500 
    Details
    ISSN: 1572-9338
    Keywords: Nonlinear programming ; sequential quadratic programming method ; numerical implementation ; test results
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract NLPQL is a FORTRAN implementation of a sequential quadratic programming method for solving nonlinearly constrained optimization problems with differentiable objective and constraint functions. At each iteration, the search direction is the solution of a quadratic programming subproblem. This paper discusses the organization of NLPQL, including the formulation of the subproblem and the information that must be provided by a user. A summary is given of the performance of different algorithmic options of NLPQL on a collection of test problems (115 hand-selected or application problems, 320 randomly generated problems). The performance of NLPQL is compared with that of some other available codes.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02022087
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  • 2
    Electronic Resource
    Electronic Resource
    Integrating modeling, algorithm design, and computational implementation to solve a large-scale non-linear mixed integer programming problem (1986)
    Springer
    Annals of operations research 5 (1986), S. 395-411 
    Details
    ISSN: 1572-9338
    Keywords: Nonlinear programming ; decomposition ; branch and bound ; network ; transportation ; mixed integer programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract This paper describes the formulation of a nonlinear mixed integer programming model for a large-scale product development and distribution problem and the design and computational implementation of a special purpose algorithm to solve the model. The results described demonstrate that integrating the art of modeling with the sciences of solution methodology and computer implementation provides a powerful approach for attacking difficult problems. The efforts described here were successful because they capitalized on the wealth of existing modeling technology and algorithm technology, the availability of efficient and reliable optimization, matrix generation and graphics software, and the speed of large-scale computer hardware. The model permitted the combined use of decomposition, general linear programming and network optimization within a branch and bound algorithm to overcome mathematical complexity. The computer system reliably found solutions with considerably better objective function values 30 to 50 times faster than had been achieved using general purpose optimization software alone. Throughout twenty months of daily use, the system was credited with providing insights and suggesting strategies that led to very large dollar savings.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02022082
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  • 3
    Electronic Resource
    Electronic Resource
    Approximation of time-dependent free boundaries (1982)
    Springer
    Numerische Mathematik 40 (1982), S. 179-199 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS) ; Primary 65N30 ; Secondary 35R35 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Two problems are considered in the paper: the first of them is connected with elliptic variational inequalities and consists in developing a moving obstacle algorithm for approximating the unknown free boundary; the other problem is linked with numerical solution of the Stefan problem, which is formulated in the similar way as in the elliptic case. Some computational aspects are also discussed in the paper.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01400538
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  • 4
    Electronic Resource
    Electronic Resource
    Finite elements for parabolic equations backwards in time (1982)
    Springer
    Numerische Mathematik 40 (1982), S. 207-227 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65M30 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Several regularization methods for parabolic equations backwards in time together with the usual additional constraints for their solution are considered. The error of the regularization is estimated from above and below. For a “boundary value problem in time”-method, finite elements as well as a time discretization are introduced and the error with respect to the regularized solution is estimated, thus giving an overall error of the discrete regularized problem. The algorithm is tested in simple numerical examples.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01400540
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  • 5
    Electronic Resource
    Electronic Resource
    A potential method for the biharmonic equation (1984)
    Springer
    Numerische Mathematik 43 (1984), S. 105-119 
    Details
    ISSN: 0945-3245
    Keywords: AMS (MOS): 65N30 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary A new formulation of the Dirichlet problem for the biharmonic operator is presented. This gives rise to a simple numerical method to solve the above problem. Convergence is proved in the unidimensional case. Numerical results in one and two dimensional test problems are presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01389641
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  • 6
    Electronic Resource
    Electronic Resource
    A uniformly convergent difference scheme for a semilinear singular perturbation problem (1984)
    Springer
    Numerische Mathematik 43 (1984), S. 175-198 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65 L 10 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We present a difference scheme for solving a semilinear singular perturbation problem with any number of turning points of arbitrary orders. It is shown that a solution of the scheme converges, uniformly in a perturbation parameter, to that of the continuous problem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01390122
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  • 7
    Electronic Resource
    Electronic Resource
    Une méthode numérique pour les problèmes d'équilibre de corps hyperélastiques compressibles en grandes déformations (1984)
    Springer
    Numerische Mathematik 43 (1984), S. 199-224 
    Details
    ISSN: 0945-3245
    Keywords: AMS (MOS): 65 N 30 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Description / Table of Contents: Summary This paper uses Augmented Lagrangian techniques for the numerical solution of equilibrium problems of compressible hyperelastic bodies subjected to large deformations. The resulting method is illustrated by several numerical examples.
    Notes: Résumé Cet article applique les techniques de Lagrangien Augmenté à la résolution numérique des problèmes d'équilibre de corps hyperélastiques compressibles soumis à de grandes déformations. La méthode obtenue est illustrée par plusieurs exemples numériques.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01390123
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  • 8
    Electronic Resource
    Electronic Resource
    Adams methods for neutral functional differential equations (1982)
    Springer
    Numerische Mathematik 39 (1982), S. 221-230 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65L05 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary In this paper Adams type methods for the special case of neutral functional differential equations are examined. It is shown thatk-step methods maintain orderk+1 for sufficiently small step size in a sufficiently smooth situation. However, when these methods are applied to an equation with a “non-smooth” solution the order of convergence is only one. Some computational considerations are given and numerical experiments are presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01408695
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  • 9
    Electronic Resource
    Electronic Resource
    Improvement of numerical solution of boundary layer problems by incorporation of asymptotic approximations (1982)
    Springer
    Numerische Mathematik 39 (1982), S. 309-324 
    Details
    ISSN: 0945-3245
    Keywords: AMS (MOS): 65L10 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary A method for improvement of the numerical solution of differential equations by incorporation of asymptotic approximations is investigated for a class of singular perturbation problems. Uniform error estimates are derived for this method when implemented in known difference schemes and applied to linear second order O.D.E.'s. An improvement by a factor ofε n+1 can be obtained (where ɛ is the “small” parameter andn is the order of the asymptotic approximation) for a small amount of extra work. Numerical experiments are presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01407865
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  • 10
    Electronic Resource
    Electronic Resource
    Finite difference methods and their convergence for a class of singular two point boundary value problems (1982)
    Springer
    Numerische Mathematik 39 (1982), S. 341-350 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65L10 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We discuss the construction of three-point finite difference approximations and their convergence for the class of singular two-point boundary value problems: (x α y′)′=f(x,y), y(0)=A, y(1)=B, 0〈α〈1. We first establish a certain identity, based on general (non-uniform) mesh, from which various methods can be derived. To obtain a method having order two for all α∈(0,1), we investigate three possibilities. By employing an appropriate non-uniform mesh over [0,1], we obtain a methodM 1 based on just one evaluation off. For uniform mesh we obtain two methodsM 2 andM 3 each based on three evaluations off. For α=0,M 1 andM 2 both reduce to the classical second-order method based on one evaluation off. These three methods are investigated, theirO(h 2)-convergence established and illustrated by numerical examples.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01407867
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