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  • 1
    Electronic Resource
    Electronic Resource
    An algorithm for determining all extreme points of a convex polytope (1977)
    Springer
    Mathematical programming 12 (1977), S. 81-96 
    Details
    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract An algorithm for determining all the extreme points of a convex polytope associated with a set of linear constraints, via the computation of basic feasible solutions to the constraints, is presented. The algorithm is based on the product-form revised simplex method and as such can be readily linked onto standard linear programming codes. Applications of such an algorithm are reviewed and limited computational experience given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01593771
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Solving the subproblem in the lagrangian dual of separable discrete programs with linear constraints (1982)
    Springer
    Mathematical programming 24 (1982), S. 107-112 
    Details
    ISSN: 1436-4646
    Keywords: Lagrangian Subproblem ; Lagrangian Duality ; Non-linear Discrete Programming ; Separable Objective Function
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract This note presents an efficient method for the routine solution of the subproblem associated with the Lagrangian dual of discrete programming problems having separable non-linear objective function and linear constraints. An additional advantage for subgradient methods is described.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01585097
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Eliminating extraneous edges in Greenberg's algorithm (1980)
    Springer
    Mathematical programming 19 (1980), S. 106-110 
    Details
    ISSN: 1436-4646
    Keywords: Convex Polyhedra ; Extreme Edges ; Degeneracy ; Extraneous Edges
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract A procedure for eliminating the extraneous edges of convex polyhedra found by Greenberg's method is presented and computational experience with it is reported.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01581632
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    A randomized algorithm for fixed-dimensional linear programming (1989)
    Springer
    Mathematical programming 44 (1989), S. 203-212 
    Details
    ISSN: 1436-4646
    Keywords: Linear programming ; randomized algorithm
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We give a (Las Vegas) randomized algorithm for linear programming in a fixed dimensiond for which the expected computation time is $$O(d^{(3 + \varepsilon _d )d} n)$$ , where lim d→∞ ε d = 0. This improves the corresponding worst-case complexity, $$O(3^{d^2 } n)$$ . The method is based on a recent idea of Clarkson. Two variations on the algorithm are examined briefly.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01587088
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    Paper (German National Licenses)
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  • 5
    Electronic Resource
    Electronic Resource
    Calculating surrogate constraints (1980)
    Springer
    Mathematical programming 19 (1980), S. 255-278 
    Details
    ISSN: 1436-4646
    Keywords: Surrogate Constraints ; Subgradient Methods ; Generalised Programming ; Surrogate Duality
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Various theoretical properties of the surrogate dual of a mathematical programming problem are discussed, including some connections with the Lagrangean dual. Two algorithms for solving the surrogate dual, suggested by analogy with Lagrangean optimisation, are described and proofs of their convergence given. A simple example is solved using each method.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01581647
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  • 6
    Electronic Resource
    Electronic Resource
    On linear programs with random costs (1986)
    Springer
    Mathematical programming 35 (1986), S. 3-16 
    Details
    ISSN: 1436-4646
    Keywords: Random linear program ; probabilistic analysis of algorithms ; average complexity ; quadratic assignment problem ; branch-and-bound
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We consider linear programs in which the objective function (cost) coefficients are independent non-negative random variables, and give upper bounds for the random minimum cost. One application shows that for quadratic assignment problems with such costs certain branch-and-bound algorithms usually take more than exponential time.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01589437
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  • 7
    Electronic Resource
    Electronic Resource
    On patching algorithms for random asymmetric travelling salesman problems (1990)
    Springer
    Mathematical programming 46 (1990), S. 361-378 
    Details
    ISSN: 1436-4646
    Keywords: Travelling salesman problem ; probabilistic analysis ; heuristics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Let the arc-lengthsL ij of a complete digraph onn vertices be independent uniform [0, 1] random variables. We consider the patching algorithm of Karp and Steele for the travelling salesman problem on such a digraph and give modifications which tighten the expected error. We extend these ideas to thek-person travelling salesman problem and also consider the case where cities can be visited more than once.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01585751
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  • 8
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    AMTRAN system design and software description (1970)
    In:  CASI
    Details
    Publication Date: 2019-06-27
    Description: Automatic Mathematical Translation language software for IBM 1130
    Keywords: COMPUTERS
    Type: NASA-CR-102834 , IESD-COMP-1171
    Format: application/pdf
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    NASA TECHNICAL REPORTS
  • 9
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    AMTRAN development program Interim report (1968)
    In:  CASI
    Details
    Publication Date: 2019-06-27
    Description: AMTRAN software system developed for IBM 1130 computer
    Keywords: COMPUTERS
    Type: NASA-CR-98362 , RL-CL-084
    Format: application/pdf
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    NASA TECHNICAL REPORTS
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