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  • Articles  (19)
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  • Linear Programming  (19)
  • 1980-1984  (19)
  • Mathematics  (19)
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  • Articles  (19)
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  • 1
    Electronic Resource
    Electronic Resource
    On the non-polynomiality of the relaxation method for systems of linear inequalities (1982)
    Springer
    Mathematical programming 22 (1982), S. 93-103 
    Details
    ISSN: 1436-4646
    Keywords: Linear Programming ; Relaxation Method ; Polynomiality
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract A class of linear programs is given in which the relaxation method for inequalities, under the same operating rules as Khacian's method, is not polynomial in the length of the input. This result holds for any value of the relaxation parameter.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01581028
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Polynomial algorithms for a class of linear programs (1981)
    Springer
    Mathematical programming 21 (1981), S. 121-136 
    Details
    ISSN: 1436-4646
    Keywords: Linear Programming ; Polynomial Algorithms ; Total Unimodularity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract This paper describes several algorithms for solution of linear programs. The algorithms are polynomial when the problem data satisfy certain conditions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01584235
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  • 3
    Electronic Resource
    Electronic Resource
    An algorithm for computing equilibria in a linear monetary economy (1981)
    Springer
    Mathematical programming 21 (1981), S. 182-189 
    Details
    ISSN: 1436-4646
    Keywords: Equilibrium ; Linear Monetary Economy ; Linear Programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract An algorithm is presented for computing equilibria in a linear monetary economy, that is, an exchange economy in which all individuals have linear utility functions and in which goods are bought and sold only in exchange for money. The algorithm computes the equilibrium prices by solving a finite sequence of linear programming problems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01584239
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  • 4
    Electronic Resource
    Electronic Resource
    Optimum matching forests II: General weights (1982)
    Springer
    Mathematical programming 22 (1982), S. 12-38 
    Details
    ISSN: 1436-4646
    Keywords: Graph ; Matching ; Branching ; Linear Programming ; Polyhedron
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Matching forests generalize branchings in a directed graph and matchings in an undirected graph. We present an efficient algorithm, the PMF Algorithm, for the problem: given a mixed graphG and a real weight on each of its edges, find a perfect matching forest of maximum weight-sum. The PMF Algorithm proves the sufficiency of a linear system which definesP = (G) andP(G), the convex hull of incidence vectors of perfect matching forests and matching forests respectively ofG. The algorithm also provides a generalization of Tutte's theorem on the existence of perfect matchings in an undirected graph.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01581023
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  • 5
    Electronic Resource
    Electronic Resource
    Computational results on an algorithm for finding all vertices of a polytope (1980)
    Springer
    Mathematical programming 18 (1980), S. 308-329 
    Details
    ISSN: 1436-4646
    Keywords: Polytopes ; Linear Programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract This paper provides answers to several questions raised by V. Klee regarding the efficacy of Mattheiss' algorithm for finding all vertices of convex polytopes. Several results relating to the expected properties of polytopes are given which indicate thatn-polytopes defined by “large” numbers of constraints are difficult to obtain by random processes, the expected value of the number of vertices of polytope is considerably less than Klee's least upper bound the expected performance of Mattheiss' algorithm is far better than Klee's upper bound would suggest.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01588326
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  • 6
    Electronic Resource
    Electronic Resource
    Optimality in transient markov chains and linear programming (1980)
    Springer
    Mathematical programming 18 (1980), S. 1-6 
    Details
    ISSN: 1436-4646
    Keywords: Discrete Dynamic Programming ; Optimal Markov Chains ; Linear Programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract It is shown how a discrete Markov programming problem can be transformed, using a linear program, into an equivalent problem from which the optimal decision rule can be trivially deduced. This transformation is applied to problems which have either transient probabilities or discounted costs.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01588291
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  • 7
    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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  • 8
    Electronic Resource
    Electronic Resource
    Optimum matching forests I: Special weights (1982)
    Springer
    Mathematical programming 22 (1982), S. 1-11 
    Details
    ISSN: 1436-4646
    Keywords: Graph ; Matching ; Branching ; Linear Programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We introduce the concept of matching forests as a generalization of branchings in a directed graph and matchings in an undirected graph. Given special weights on the edges of a mixed graph, we present an efficient algorithm for finding an optimum weight-sum matching forest. The algorithm is a careful application of known branching and matching algorithms. The maximum cardinality matching forest problem is solved as a special case.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01581022
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  • 9
    Electronic Resource
    Electronic Resource
    An implementation of the simplex method for linear programming problems with variable upper bounds (1982)
    Springer
    Mathematical programming 23 (1982), S. 34-49 
    Details
    ISSN: 1436-4646
    Keywords: Linear Programming ; Variable Upper Bounds ; Degeneracy ; Triangular Factorization
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Special methods for dealing with constraints of the formx j ≤ x k , called variable upper bounds, were introduced by Schrage. Here we describe a method that circumvents the massive degeneracy inherent in these constraints and show how it can be implemented using triangular basis factorizations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01583778
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  • 10
    Electronic Resource
    Electronic Resource
    Solving staircase linear programs by the simplex method, 1: Inversion (1982)
    Springer
    Mathematical programming 23 (1982), S. 274-313 
    Details
    ISSN: 1436-4646
    Keywords: Large-Scale Optimization ; Linear Programming ; Staircase Linear Programs ; Simplex Method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract This and a companion paper consider how current implementations of the simplex method may be adapted to better solve linear programs that have a staged, or ‘staircase’, structure. The present paper looks at ‘inversion’ routines within the simplex method, particularly those for sparse triangular factorization of a basis by Gaussian elimination and for solution of triangular linear systems. The succeeding paper examines ‘pricing’ routines. Both papers describe extensive (though preliminary) computational experience, and can point to some quite promising results.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01583795
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