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  • Linear programming  (10)
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  • 1988  (10)
  • Mathematik  (10)
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  • Artikel  (10)
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  • 1995-1999
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  • 1
    Digitale Medien
    Digitale Medien
    Springer
    Mathematical programming 42 (1988), S. 391-405 
    ISSN: 1436-4646
    Schlagwort(e): Linear programming ; large-scale-systems ; decomposition ; parallel computing
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract This paper describes DECOMPAR: an implementation of the Dantzig-Wolfe decomposition algorithm for block-angular linear programs using parallel processing of the subproblems. The software is based on a robust experimental code for LP decomposition and runs on the CRYSTAL multicomputer at the University of Wisconsin-Madison. Initial computational experience is reported. Promising directions in future development of this approach are discussed.
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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  • 2
    Digitale Medien
    Digitale Medien
    Springer
    Mathematical programming 40 (1988), S. 59-93 
    ISSN: 1436-4646
    Schlagwort(e): Linear programming ; interior method ; computational complexity ; Newton's method
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract A new interior method for linear programming is presented and a polynomial time bound for it is proven. The proof is substantially different from those given for the ellipsoid algorithm and for Karmarkar's algorithm. Also, the algorithm is conceptually simpler than either of those algorithms.
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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  • 3
    Digitale Medien
    Digitale Medien
    Springer
    Mathematical programming 41 (1988), S. 61-71 
    ISSN: 1436-4646
    Schlagwort(e): Linear programming ; Karmarkar's method ; Cholesky factorization ; rank-one updates
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract The paper presents a numerical method for computing the projections for Karmarkar's new algorithm for linear programming. The method is simple to implement, fully exploits sparsity, and appears in limited experimentation to have good stability properties. Preliminary numerical experience indicates that the method promises advantages over methods that refactor a matrix at every iteration.
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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  • 4
    Digitale Medien
    Digitale Medien
    Springer
    Mathematical programming 41 (1988), S. 385-392 
    ISSN: 1436-4646
    Schlagwort(e): Linear programming ; simplex method ; degeneracy ; scheduling
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract The solution of scheduling problems often gives rise to highly degenerate linear programmes which cause significant computational difficulties for the revised simplex method. Wolfe's highly effective “ad hoc” method for overcoming the cycling or stalling problems associated with degeneracy is described. Here it is given a geometric interpretation in terms of finding a direction of recession for a reduced problem which is fundamental to a full understanding of the procedure. An example of an aircrew scheduling problem is used to illustrate the effectiveness of the method.
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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  • 5
    Digitale Medien
    Digitale Medien
    Springer
    Mathematical programming 41 (1988), S. 367-373 
    ISSN: 1436-4646
    Schlagwort(e): Linear programming ; interior algorithm ; central trajectory ; barrier function ; Newton's method
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract In this note we report a simple characteristic of linear programming central trajectories which has a surprising consequence. Specifically, we show that given a bounded polyhedral setP with nonempty interior, the logarithmic barrier function (with no objective component) induces a vector field of negative Newton directions which flows from the center ofP, along central trajectories, to solutions of every possible linear program onP.
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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  • 6
    Digitale Medien
    Digitale Medien
    Springer
    Mathematical programming 41 (1988), S. 97-113 
    ISSN: 1436-4646
    Schlagwort(e): Linear programming ; Karmarkar's algorithm ; special structure
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract We propose methods to take advantage of specially-structured constraints in a variant of Karmarkar's projective algorithm for standard form linear programming problems. We can use these constraints to generate improved bounds on the optimal value of the problem and also to compute the necessary projections more efficiently, while maintaining the theoretical bound on the algorithm's performance. It is shown how various upper-bounding constraints can be handled implicitly in this way. Unfortunately, the situation for network constraints appears less favorable.
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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  • 7
    Digitale Medien
    Digitale Medien
    Springer
    Annals of operations research 14 (1988), S. 1-16 
    ISSN: 1572-9338
    Schlagwort(e): Linear programming ; planning under uncertainty ; large-scale systems ; parallel processors ; stochastic programming ; decomposition principle
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik , Wirtschaftswissenschaften
    Notizen: Abstract Industry and government routinely solve deterministic mathematical programs for planning and schelduling purposes, some involving thousands of variables with a linear or non-linear objective and inequality constraints. The solutions obtained are often ignored because they do not properly hedge against future contingencies. It is relatively easy to reformulate models to include uncertainty. The bottleneck has been (and is) our capability to solve them. The time is now ripe for finding a way to do so. To this end, we describe in this paper how large-scale system methods for solving multi-staged systems, such as Bender's Decomposition, high-speed sampling or Monte Carlo simulation, and parallel processors can be combined to solve some important planning problems involving uncertainty. For example, parallel processors may make it possible to come to better grips with the fundamental problems of planning, scheduling, design, and control of complex systems such as the economy, an industrial enterprise, an energy system, a water-resource system, military models for planning-and-control, decisions about investment, innovation, employment, and health-delivery systems.
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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  • 8
    Digitale Medien
    Digitale Medien
    Springer
    Mathematical programming 41 (1988), S. 281-315 
    ISSN: 1436-4646
    Schlagwort(e): Linear programming ; simplex methods ; piecewise-linear programming ; nondifferentiable optimization
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract The simplex method for linear programming can be extended to permit the minimization of any convex separable piecewise-linear objective, subject to linear constraints. Part I of this paper has developed a general and direct simplex algorithm for piecewise-linear programming, under convenient assumptions that guarantee a finite number of basic solutions, existence of basic feasible solutions, and nondegeneracy of all such solutions. Part II now shows how these assumptions can be weakened so that they pose no obstacle to effective use of the piecewise-linear simplex algorithm. The theory of piecewise-linear programming is thereby extended, and numerous features of linear programming are generalized or are seen in a new light. An analysis of the algorithm's computational requirements and a survey of applications will be presented in Part III.
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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  • 9
    Digitale Medien
    Digitale Medien
    Springer
    Mathematical programming 40 (1988), S. 289-315 
    ISSN: 1436-4646
    Schlagwort(e): Linear programming ; Karmarkar's method ; inexact projections
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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  • 10
    Digitale Medien
    Digitale Medien
    Springer
    Journal of mathematical biology 26 (1988), S. 193-197 
    ISSN: 1432-1416
    Schlagwort(e): Optimisation ; Leslie matrix ; Equilibrium ; Linear programming ; Nonlinear
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The problem of optimal harvesting in equilibrium is considered in a Leslie matrix model in which both mortality and fecundity in all age-classes may be density-dependent. The conclusion is that the optimal strategy is of the two-age-class type, in common with results obtained previously for simpler models.
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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