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  • Articles  (5)
  • Integer Programming  (5)
  • 1975-1979  (5)
  • 1945-1949
  • 1979  (5)
  • Mathematics  (5)
  • Sociology
  • Architecture, Civil Engineering, Surveying
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  • Articles  (5)
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  • 1975-1979  (5)
  • 1945-1949
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  • Mathematics  (5)
  • Sociology
  • Architecture, Civil Engineering, Surveying
  • Computer Science  (5)
  • 1
    Electronic Resource
    Electronic Resource
    Efficient group cuts for integer programs (1979)
    Springer
    Mathematical programming 17 (1979), S. 176-183 
    Details
    ISSN: 1436-4646
    Keywords: Integer Programming ; Column Generation ; Group Theoretic Method ; Lagrangian ; Group Cuts ; Generalized Linear Programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Gomory's group relaxation for integer programs has been refined by column generation methods and dual ascent algorithms to identify a set of candidate solutions which are feasible in the relaxation but not necessarily so in the original integer program. Attempts at avoiding branch and bound procedures at this point have focussed on providing extra group constraints which eliminate all or most of the candidate solutions so that further ascent can take place. It will be shown that a single constraint usually of order 2 or 3, can eliminate all of the candidate solutions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01588242
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    A o(n logn) algorithm for LP knapsacks with GUB constraints (1979)
    Springer
    Mathematical programming 17 (1979), S. 345-361 
    Details
    ISSN: 1436-4646
    Keywords: Integer Programming ; Knapsack Problems ; Multiple Choice ; Surrogate Constraints
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract A specialization of the dual simplex method is developed for solving the linear programming (LP) knapsack problem subject to generalized upper bound (GUB) constraints. The LP/GUB knapsack problem is of interest both for solving more general LP problems by the dual simplex method, and for applying surrogate constraint strategies to the solution of 0–1 “Multiple Choice” integer programming problems. We provide computational bounds for our method of o(n logn), wheren is the total number of problem variables. These bounds reduce the previous best estimate of the order of complexity of the LP/GUB knapsack problem (due to Witzgall) and provide connections to computational bounds for the ordinary knapsack problem. We further provide a variant of our method which has only slightly inferior worst case bounds, yet which is ideally suited to solving integer multiple choice problems due to its ability to post-optimize while retaining variables otherwise weeded out by convex dominance criteria.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01588255
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Some relationships between lagrangian and surrogate duality in integer programming (1979)
    Springer
    Mathematical programming 17 (1979), S. 320-334 
    Details
    ISSN: 1436-4646
    Keywords: Integer Programming ; Surrogate Duality ; Lagrangian Relaxation ; Lagrangian Duality ; Surrogate Constraint
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Lagrangian dual approaches have been employed successfully in a number of integer programming situations to provide bounds for branch-and-bound procedures. This paper investigates some relationship between bounds obtained from lagrangian duals and those derived from the lesser known, but theoretically more powerful surrogate duals. A generalization of Geoffrion's integrality property, some complementary slackness relationships between optimal solutions, and some empirical results are presented and used to argue for the relative value of surrogate duals in integer programming. These and other results are then shown to lead naturally to a two-phase algorithm which optimizes first the computationally easier lagrangian dual and then the surrogate dual.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01588253
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  • 4
    Electronic Resource
    Electronic Resource
    Theory and algorithms for linear multiple objective programs with zero–one variables (1979)
    Springer
    Mathematical programming 17 (1979), S. 362-390 
    Details
    ISSN: 1436-4646
    Keywords: Zero–one Multiple Objective Programs ; Multi-Criteria Optimization ; Multiple Objective Optimization ; Efficient Points ; Vector Optimization ; Integer Programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract A new algorithm and theoretical results are presented for linear multiple objective programs with zero–one variables. A procedure to identify strong and weak efficient points as well as an extension of the main problem are analyzed. Extensive computational results are given and several topics for further research are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01588256
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  • 5
    Electronic Resource
    Electronic Resource
    Minimal inequalities (1979)
    Springer
    Mathematical programming 17 (1979), S. 1-15 
    Details
    ISSN: 1436-4646
    Keywords: Integer Programming ; Cutting-planes ; Subadditivity ; Group Problem
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We provide a characterization of minimal inequalities for bounded mixed integer programs, in terms of subadditive functions. The condition on the columns of the integer-constrained variables is analogous to that obtained earlier for the group problem, and we also determine the condition on the columns of the continuous variables.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01588222
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