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  • 1
    Electronic Resource
    Electronic Resource
    Conjugate Gradient Method for Nonlinear Programming Problems with Linear Constraints (1968)
    s.l. : American Chemical Society
    Industrial and engineering chemistry 7 (1968), S. 142-151 
    Details
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1021/i160025a024
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Matrix factorizations in optimization of nonlinear functions subject to linear constraints — an addendum (1977)
    Springer
    Mathematical programming 12 (1977), S. 279-280 
    Details
    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01593793
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Strongly polynomial dual simplex methods for the maximum flow problem (1998)
    Springer
    Mathematical programming 80 (1998), S. 17-33 
    Details
    ISSN: 1436-4646
    Keywords: Dual simplex method ; Maximum flow ; Strongly polynomial ; Preflow algorithm ; Valid distance labels
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract This paper presents dual network simplex algorithms that require at most 2nm pivots and O(n 2 m) time for solving a maximum flow problem on a network ofn nodes andm arcs. Refined implementations of these algorithms and a related simplex variant that is not strictly speaking a dual simplex algorithm are shown to have a complexity of O(n 3). The algorithms are based on the concept of apreflow and depend upon the use of node labels that are underestimates of the distances from the nodes to the sink node in the extended residual graph associated with the current flow. © 1998 The Mathematical Programming Society, Inc. Published by Elsevier Science B.V.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01582129
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    Modifications and implementation of the ellipsoid algorithm for linear programming (1982)
    Springer
    Mathematical programming 23 (1982), S. 1-19 
    Details
    ISSN: 1436-4646
    Keywords: Ellipsoid Algorithm ; Linear Programming ; Polynomial Boundedness ; Khachian's Method ; Linear Inequalities
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We give some modifications of the ellipsoid algorithm for linear programming and describe a numerically stable implementation. We are concerned with practical problems where user-supplied bounds can usually be provided. Our implementation allows constraint dropping and updates bounds on the optimal value, and should be able to terminate with an indication of infeasibility or with a provably good feasible solution in a moderate number of iterations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01583776
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    Paper (German National Licenses)
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  • 5
    Electronic Resource
    Electronic Resource
    Curvilinear path steplength algorithms for minimization which use directions of negative curvature (1980)
    Springer
    Mathematical programming 18 (1980), S. 31-40 
    Details
    ISSN: 1436-4646
    Keywords: Step-size Procedures ; Line Search ; Gradient Methods ; Unconstrained Minimization ; Negative Curvature
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract The Armijo and Goldstein step-size rules are modified to allow steps along a curvilinear path of the formx(α) + x + αs + α2 d, wherex is the current estimate of the minimum,s is a descent direction andd is a nonascent direction of negative curvature. By using directions of negative curvature when they exist, we are able to prove, under fairly mild assumptions, that the sequences of iterates produced by these algorithms converge to stationary points at which the Hessian matrix of the objective function is positive semidefinite.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01588294
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    Paper (German National Licenses)
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  • 6
    Electronic Resource
    Electronic Resource
    Steepest-edge simplex algorithms for linear programming (1992)
    Springer
    Mathematical programming 57 (1992), S. 341-374 
    Details
    ISSN: 1436-4646
    Keywords: Steepest-edge simplex method ; large-scale linear programming ; Devex variants
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We present several new steepest-edge simplex algorithms for solving linear programming problems, including variants of both the primal and the dual simplex method. These algorithms differ depending upon the space in which the problem is viewed as residing, and include variants in which this space varies dynamically. We present computational results comparing steepest-edge simplex algorithms and approximate versions of them against simplex algorithms that use standard pivoting rules on truly large-scale realworld linear programs with as many as tens of thousands of rows and columns. These results demonstrate unambiguously the superiority of steepest-edge pivot selection criteria to other pivot selection criteria in the simplex method.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01581089
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    Paper (German National Licenses)
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  • 7
    Electronic Resource
    Electronic Resource
    Exploiting special structure in a primal—dual path-following algorithm (1993)
    Springer
    Mathematical programming 58 (1993), S. 33-52 
    Details
    ISSN: 1436-4646
    Keywords: Interior point method ; primal—dual path-following algorithm ; structured linear programs
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract A primal-dual path-following algorithm that applies directly to a linear program of the form, min{c t x∣Ax = b, Hx ⩽u, x ⩾ 0,x ∈ ℝ n }, is presented. This algorithm explicitly handles upper bounds, generalized upper bounds, variable upper bounds, and block diagonal structure. We also show how the structure of time-staged problems and network flow problems can be exploited, especially on a parallel computer. Finally, using our algorithm, we obtain a complexity bound of O( $$\sqrt n $$ ds 2 log(nk)) fortransportation problems withs origins,d destinations (s 〈d), andn arcs, wherek is the maximum absolute value of the input data.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01581258
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    Paper (German National Licenses)
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  • 8
    Electronic Resource
    Electronic Resource
    Matrix factorizations in optimization of nonlinear functions subject to linear constraints (1976)
    Springer
    Mathematical programming 10 (1976), S. 1-31 
    Details
    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Several ways of implementing methods for solving nonlinear optimization problems involving linear inequality and equality constraints using numerically stable matrix factorizations are described. The methods considered all follow an active constraint set approach and include quadratic programming, variable metric, and modified Newton methods.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01580651
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    Paper (German National Licenses)
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  • 9
    Electronic Resource
    Electronic Resource
    A computational comparison of the dinic and network simplex methods for maximum flow (1988)
    Springer
    Annals of operations research 13 (1988), S. 81-123 
    Details
    ISSN: 1572-9338
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract We study the implementation of two fundamentally different algorithms for solving the maximum flow problem: Dinic's method and the network simplex method. For the former, we present the design of a storage-efficient implementation. For the latter, we develop a "steepest-edge" pivot selection criterion that is easy to include in an existing network simplex implementation. We compare the computational efficiency of these two methods on a personal computer with a set of generated problems of up to 4 600 nodes and 27 000 arcs.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02288321
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    Paper (German National Licenses)
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  • 10
    Electronic Resource
    Electronic Resource
    A relaxed version of Karmarkar's method (1988)
    Springer
    Mathematical programming 40 (1988), S. 289-315 
    Details
    ISSN: 1436-4646
    Keywords: Linear programming ; Karmarkar's method ; inexact projections
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract A relaxed version of Karmarkar's method is developed. This method is proved to have the same polynomial time complexity as Karmarkar's method and its efficient implementation using inexact projections is discussed. Computational results obtained using a preliminary implementation of the method are presented which indicate that the method is practicable.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01580737
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    Paper (German National Licenses)
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