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1.
In this paper, we will propose algorithms for calculating a minimal ellipsoid circumscribing a polytope defined by a system
of linear inequalities. If we know all vertices of the polytope and its cardinality is not very large, we can solve the problem
in an efficient manner by a number of existent algorithms. However, when the polytope is defined by linear inequalities, these
algorithms may not work since the cardinality of vertices may be huge. Based on a fact that vertices determining an ellipsoid
are only a fraction of these vertices, we propose algorithms which iteratively calculate an ellipsoid which covers a subset
of vertices. Numerical experiment shows that these algorithms perform well for polytopes of dimension up to seven. 相似文献
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Upper bounds for survival probability of the contact process 总被引:3,自引:0,他引:3
5.
This paper proposes a two step algorithm for solving a large scale semi-definite logit model, which is appreciated as a powerful
model in failure discriminant analysis. This problem has been successfully solved by a cutting plane (outer approximation)
algorithm. However, it requires much more computation time than the corresponding linear logit model. A two step algorithm
to be proposed in this paper is intended to reduce the amount of computation time by eliminating a certain portion of the
data based on the information obtained by solving an associated linear logit model. It will be shown that this algorithm can
generate a solution with almost the same quality as the solution obtained by solving the original large scale semi-definite
model within a fraction of computation time. 相似文献
6.
Hiroshi Konno 《Mathematical Programming》1988,41(1-3):185-193
We will consider a concave minimization problem associated with a series production system in which raw material is processed inm consecutive facilities. The products at some facility are either sent to the next facility or stocked in the warehouse. The amount of demand for the final products during periodi, i = 1,,n, are known in advance. Our problem is to minimize the sum of processing, holding and backlogging cost, all of which are assumed to be concave.The origin of this model is the classical economic lot size problem of Wagner and Whitin and was extensively studied by Zangwill. This model is very important from the theoretical as well as practical point of view and this is one of the very rare instances in which polynomial time algorithm has been constructed for concave minimization problems.The purpose of this paper is to extend the model further to the situation in which time lag is associated with processing at each facility. We will propose an efficient O(n
4
m) algorithm for this class of problems. 相似文献
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