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  • Articles  (577)
  • Springer  (577)
  • American Chemical Society (ACS)
  • 1980-1984  (577)
  • 1982  (577)
  • Computer Science  (577)
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  • Articles  (577)
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  • 1980-1984  (577)
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  • 1
    Electronic Resource
    Electronic Resource
    On the use of penumbras in blocking and antiblocking theory (1982)
    Springer
    Mathematical programming 22 (1982), S. 71-81 
    Details
    ISSN: 1436-4646
    Keywords: Blocking ; Antiblocking ; Polarity ; Penumbra
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract E. Johnson has recently shown that the concept of a penumbra leads to a simple geometric description of the blocker and antiblocker of a given set. Here we develop some basic results on penumbras which permit us to slightly generalize and simplify results on their relationship to blocking and antiblocking theory. In addition, motivated by the obvious symmetry of our results, we examine the effect of reversing the blocking and antiblocking operations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01581026
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  • 2
    Electronic Resource
    Electronic Resource
    On the structure of all minimum cuts in a network and applications (1982)
    Springer
    Mathematical programming 22 (1982), S. 121-121 
    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/BF01581031
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  • 3
    Electronic Resource
    Electronic Resource
    Heuristics for the fixed cost median problem (1982)
    Springer
    Mathematical programming 22 (1982), S. 148-162 
    Details
    ISSN: 1436-4646
    Keywords: Set Covering Problem ; Median Problem ; Location Problems ; Heuristics ; Worst Case Analysis ; Continuous Location Problem
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We describe in this paper polynomial heuristics for three important hard problems—the discrete fixed cost median problem (the plant location problem), the continuous fixed cost median problem in a Euclidean space, and the network fixed cost median problem with convex costs. The heuristics for all the three problems guarantee error ratios no worse than the logarithm of the number of customer points. The derivation of the heuristics is based on the presentation of all types of median problems discussed as a set covering problem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01581035
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  • 4
    Electronic Resource
    Electronic Resource
    On minimax optimization problems (1982)
    Springer
    Mathematical programming 22 (1982), S. 227-230 
    Details
    ISSN: 1436-4646
    Keywords: Minimax ; Nonconvex Optimization ; Stationary Points
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We give a short proof that in a convex minimax optimization problem ink dimensions there exist a subset ofk + 1 functions such that a solution to the minimax problem with thosek + 1 functions is a solution to the minimax problem with all functions. We show that convexity is necessary, and prove a similar theorem for stationary points when the functions are not necessarily convex but the gradient exists for each function.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01581038
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  • 5
    Electronic Resource
    Electronic Resource
    On the differential properties of the support function of the∈-subdifferential of a convex function (1982)
    Springer
    Mathematical programming 24 (1982), S. 257-268 
    Details
    ISSN: 1436-4646
    Keywords: Nondifferentiable Programming ; Convex Analysis ; Sensivity Analysis ; Duality Theory ; Second Order Derivative ; Second Order Methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We study differential properties of the support function of the∈-subdifferential of a convex function; applications in algorithmics are also given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01585110
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  • 6
    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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  • 7
    Electronic Resource
    Electronic Resource
    Boolean sublattices connected with minimization problems on matroids (1982)
    Springer
    Mathematical programming 22 (1982), S. 117-120 
    Details
    ISSN: 1436-4646
    Keywords: Augmenting Path Algorithm ; Boolean Lattice ; Jordan-Hölder Theorem ; Matroid Intersection
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract It is noted that the decomposition of a network presented by J.C. Picard and M. Queyranne through an algorithmic argument may be defined from a general lattice-theoretic result for more general problems for which the equalities of maximum-flow minimum-cut type hold.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01581030
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  • 8
    Electronic Resource
    Electronic Resource
    On the computational utility of posynomial geometric programming solution methods (1982)
    Springer
    Mathematical programming 22 (1982), S. 163-201 
    Details
    ISSN: 1436-4646
    Keywords: Geometric Programming ; Code Comparisons ; Numerical Testing ; Nonlinear Programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Ten codes or code variants were used to solve the five equivalent posynomial GP problem formulations. Four of these codes were general NLP codes; six were specialized GP codes. A total of forty-two test problems was solved with up to twenty randomly generated starting points per problem. The convex primal formulation is shown to be intrinsically easiest to solve. The general purpose GRG code called OPT appears to be the most efficient code for GP problem solution. The reputed superiority of the specialized GP codes GGP and GPKTC appears to be largely due to the fact that these codes solve the convex primal formulation. The dual approaches are only likely to be competitive for small degree of difficulty, tightly constrained problems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01581036
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  • 9
    Electronic Resource
    Electronic Resource
    A polynomial algorithm for integer programming covering problems satisfying the integer round-up property (1982)
    Springer
    Mathematical programming 22 (1982), S. 231-235 
    Details
    ISSN: 1436-4646
    Keywords: Integer Programming ; Covering
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract LetA be a non-negative matrix with integer entries and no zero column. The integer round-up property holds forA if for every integral vectorw the optimum objective value of the generalized covering problem min{1y: yA ≥ w, y ≥ 0 integer} is obtained by rounding up to the nearest integer the optimum objective value of the corresponding linear program. A polynomial time algorithm is presented that does the following: given any generalized covering problem with constraint matrixA and right hand side vectorw, the algorithm either finds an optimum solution vector for the covering problem or else it reveals that matrixA does not have the integer round-up property.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01581039
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  • 10
    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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