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71.
Israel Zang 《Mathematical Programming》1978,15(1):36-52
The gradient path of a real valued differentiable function is given by the solution of a system of differential equations. For a quadratic function the above equations are linear, resulting in a closed form solution. A quasi-Newton type algorithm for minimizing ann-dimensional differentiable function is presented. Each stage of the algorithm consists of a search along an arc corresponding to some local quadratic approximation of the function being minimized. The algorithm uses a matrix approximating the Hessian in order to represent the arc. This matrix is updated each stage and is stored in its Cholesky product form. This simplifies the representation of the arc and the updating process. Quadratic termination properties of the algorithm are discussed as well as its global convergence for a general continuously differentiable function. Numerical experiments indicating the efficiency of the algorithm are presented. 相似文献
72.
The concept of multitasking mathematical programs is discussed, and an application of multitasking to the multiple-cost-row linear programming problem is considered. Based on this, an algorithm for solving the Linear Complementarity Problem (LCP) in parallel is presented. A variety of computational results are presented using this multitasking approach on the CRAY X-MP/48. These results were obtained for randomly generated LCP's where thenxn dense matrixM has no special properties (hence, the problem is NP-hard). based on these results, an average time performance ofO(n
4) is observed. 相似文献
73.
A finite algorithm is presented in this study for solving Bilinear programs. This is accomplished by developing a suitable cutting plane which deletes at least a face of a polyhedral set. At an extreme point, a polar cut using negative edge extensions is used. At other points, disjunctive cuts are adopted. Computational experience on test problems in the literature is provided.This paper is based upon work supported by the National Science Foundation under Grant No. ENG-77-23683. 相似文献
74.
This paper reports on an experimental study of the distribution of the length of simplex paths for the Optimal Assignment
Problem. We study the distribution of the pivot counts for a version of the simplex method that with essentially equal probabilities
introduces any variable with negative reduced cost into the basis.
In this situation the distribution of the pivot counts turns out to be normally distributed and independent of the actual
cost coefficients, provided these are sufficiently spread out. Further, the mean and standard deviation grow only moderately
with the size of the problem, namely asd
1.8, andd
1.5 respectively for ad×d problem, implying in particular that the pivot counts concentrate around the mean with growingd.
The usual simplex method on the other hand gives a growth ofd
1.6. Hence a large part of the favourable polynomial growth experienced on practical problems may be attributed to the fact that
the simplex paths are rather short on the average, at least for assignment problems. 相似文献
75.
Gur Huberman 《Mathematical Programming》1983,26(1):100-108
Applied mathematical programming problems are often approximations of larger, more detailed problems. One criterion to evaluate
an approximating program is the magnitude of the difference between the optimal objective values of the original and the approximating
program. The approximation we consider is variable aggregation in a convex program. Bounds are derived on the difference between
the two optimal objective values. Previous results of Geoffrion and Zipkin are obtained by specializing our results to linear
programming. Also, we apply our bounds to a convex transportation problem.
Thanks are due to Ron Dembo, Paul Zipkin and the referees for valuable comments. This research was supported by NSF Grant
ENG-76-15599. 相似文献
76.
J. -C. Pomerol 《Mathematical Programming》1984,30(2):238-241
We show that the limiting infisup theorem of Blair, Duffin and Jeroslow (1982) is a consequence of the classical bifunctional
duality. By doing so we generalize their results and prove another limiting infisup theorem for convex quasi-concave functions. 相似文献
77.
H. P. Williams 《Mathematical Programming》1978,14(1):325-331
Two practical problems are described, each of which can be formulated in more than one way as a mixed integer programming problem. The computational experience with two formulations of each problem is given. It is pointed out how in each case a reformulation results in the associated linear programming problem being more constrained. As a result the reformulated mixed integer problem is easier to solve. The problems are a multi-period blending problem and a mining investment problem. 相似文献
78.
In this paper we develop a method for finding all efficient extreme points for multiple objective linear programs. Simple characterizations of the efficiency of an edge incident to a nondegenerate or a degenerate efficient vertex are given. These characterizations form the basis of an algorithm for enumerating all efficient vertices. The algorithm appears to have definite computational advantages over other methods. Some illustrative examples are included. 相似文献
79.
C. Roger Glassey 《Mathematical Programming》1978,14(1):98-107
When supply and demand curves for a single commodity are approximately linear in each ofN regions and interregional transportation costs are linear, then equilibrium trade flows can be computed by solving a quadratic program of special structure. An equilibrium trade flow exists in which the routes carrying positive flow form a forest, and this solution can be efficiently computed by a tree growing algorithm. 相似文献
80.
Optimal stopping,exponential utility,and linear programming 总被引:1,自引:0,他引:1
This paper uses linear programming to compute an optimal policy for a stopping problem whose utility function is exponential. This is done by transforming the problem into an equivalent one having additive utility and nonnegative (not necessarily substochastic) transition matrices.Research was supported by NSF Grant ENG 76-15599. 相似文献